- Oct 2019
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Magnetic Field Created by a Long Straight Current-Carrying Wire: Right Hand Rule 2
Will mention in Session 20 or 21.
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Magnetic field lines are continuous, forming closed loops
Always true, unlike electric field lines. There are electric monopoles, e.g., proton and electron, with porcupine and anti-porcupine field lines. There are looped \(\vec{E}\) field lines starting with a dipole array.
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Magnetic field lines can never cross
Ditto with \(\vec{E}\) field lines
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The strength of the field is proportional to the closeness of the lines.
Flux again.
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The direction of the magnetic field is tangent to the field line at any point in space. A small compass will point in the direction of the field line.
Good -- similar to our idea about electric field lines.
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enabled him to create his revolutionary theory of relativity
NOT
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crudely
crude indeed. As far as we can tell, electrons have no structure, so saying that it spins on an axis like a planet is very crude. We make do, saying that the electron has intrinsic spin angular momentum, \(\plusmn \frac{\hbar}{2}\)
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Electromagnetism is the use of electric current to make magnets.
Moving charge is the source of the magnetic field.
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they can also be magnetized
Any large structure built of steel, like a building of steel girders or a warship, can be magnetized by pounding the steel: pile drivers, riveters, etc. Liberty ship, keel plates
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Ferromagnets
This topic should follow "Electromagnets" because we understood electromagnets a century earlier than we savvied ferromagnetism (iron atoms as tiny electromagnets).
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sunspots always occur in pairs that are north and south magnetic pole
Check for paired white-and-black spots on the Sun's magnetogram. The Sun is pretty quiet now, however.
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Figure 2.
So the magnetic pole up in arctic Canada is actually an S!!
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Further experimentation shows that it is impossible to separate north and south poles in the manner that + and − charges can be separated.
Might be no such thing as a magnetic monopole. Magnets seem only to come as dipoles.
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All electric motors, with uses as diverse as powering refrigerators, starting cars, and moving elevators, contain magnets. Generators, whether producing hydroelectric power or running bicycle lights, use magnetic fields.
We can thank Michael Faraday for these developments.
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small scale
WHat an understatement! Transistors on various electronics chips are on the order of a few dozen nanometers!
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pressbooks.online.ucf.edu pressbooks.online.ucf.edu
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Discharging a Capacitor
Check the Session 18 extension in YouTube.
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the time constant for an circuit
The circuit's "time constant" \(\tau = RC\) is related to the half-life of the circuit. Both terms are used by scientists in exponentially growing or decaying systems.
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pressbooks.online.ucf.edu pressbooks.online.ucf.edu
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Combinations of Series and Parallel
Will be helpful when working on HW 2.
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Figure 4. This combination
We will work out a few like this on Friday, 10/4.
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by connecting wires having negligible resistance
idealization
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Power is energy per unit time (watts)
So after an amount of time \(\Delta t\), all of the energy of a battery will dissipate at the circuit element, e.g., the light bulb, where stored Joules from the battery are dissipated as light and heat. At that point, the bulb goes cold.
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Since all of the current must pass through each resistor, it experiences the resistance of each
Conservation of current.
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Thus the energy supplied by the source is , while that dissipated by the resistors
better
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the loss of electrical power, called a voltage drop,
NO! NO! NO! Voltage is measured in \(\frac{Joule}{Coulomb}\) but power is different, \(\frac{Joule}{second}\)!!
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Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially.
Nice definition
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Figure 1. (a) A series connection of resistors. (b) A parallel connection of resistors.
We will have discussions about these diagrams on Friday, 10/4.
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electromotive force, abbreviated emf
This term traces way back to the 1800s, before we had figured out everything and unified the electromagnetic theory. So calling it a force is anachronistic, but we still use it for the sake of custom. The common symbol is an upper case script E, \(\mathcal{E}\)
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pressbooks.online.ucf.edu pressbooks.online.ucf.edu
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the relationship of power to resistance
This is what scientists and engineers call \(I^2R\) heating, a.k.a., Joule heating. Cf., Ch. 21.3
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A tidal force results from the unequal gravitational pull on two sides of a body.
Mentioned in Lecture 14, Fall 2019
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- Sep 2019
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He was thinking about momentum! In the momentum view, the skateboarders’ values actually are equal in magnitude, though their vectors have opposite directions, positive for rightward, negative for leftward.
This was as far as the reading went to prepare for Exam 1. The sections after this will be on Exam 2!
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A power transmission line is hung from metal towers with glass insulators having a resistance of . What current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)
We will work out this exercise in Session 13, if possible
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pipe
a pipe filled with gravel
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inversely
more current that gets through to the device, less resistance.
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transfer energy
Dissipation of energy into the metallic lattice of the conductors, not to the hair dryer or other device hooked up to the circuit.
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Such a linear relationship doesn’t always occur.
For instance, in the solar corona, positive ions, protons and electrons are flying around in "current sheets" blazing through the corona, and we have a hard time figuring out the Ohmic resistance for such complicated currents. YouTube
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pressbooks.online.ucf.edu pressbooks.online.ucf.edu20.1 Current17
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Repeat the above example on Example 3, but for a wire made of silver and given there is one free electron per silver atom.
Will work this out in Session 13
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The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move Avogadro’s number () of electrons at this rate?
Good problem to try out.
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During open-heart surgery
also out of place
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(a) A defibrillator sends a 6.00-A current through the chest of a patient by applying a 10,000-V potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use this equation for power: .)
This problem is slightly out of place... might be better in a later section of Ch. 20
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signal moves
information....
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find
Big number, \(8.342\times 10^{28}\), but a few feet of 12 gauge wire is not nearly one cubic meter.
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diameter of 2.053 mm
A specification of manufacture.
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Example 3: Calculating Drift Velocity in a Common Wire
We will work through a calculation like this in Session 13, 9/25/19.
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The density of charge in a system cannot easily be increased,
a lot like water, which is pretty much an incompressible fluid
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on the order of .
less than 1 millimeter per second!
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speed of light
$$c=3\times 10^8 \frac{m}{s}$$
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Negative charges move in the direction opposite to the electric field.
We can do all of our calculations etc. with conventional current \(I\left(t\right)\), but when actually trying to understand what is physically moving so that you can capture it or track it, you have to think about electrons, if you are in a regular circuit. Electrons require "reverse psychology."
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Franklin
and everyone else until about 1899
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appliances
E.g., Kenmore 81422 washer/dryer, minimum circuit rating: 20 Amps.
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fuses and circuit breakers rated in amperes (or amps)
Cf., for example, the BP-ATM-15-RP fuse for Ford F-150,
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is the amount of charge passing through a given area in time .
refer to Fig. 1
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rate at which charge flows
"...rate at which charge flows" past a given point in a conductor, $$\frac{\Delta q}{\Delta t}$$
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electric
although the photo is a water current! 🤦🏻♂️
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Capacitors
The authors should title this section, "19.7 Energy Stored in Defibrillators" ; )
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In open heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of stored charge.
basic
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(a) What is the energy stored in the capacitor of a heart defibrillator charged to ? (b) Find the amount of stored charge.
A basic question
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The first charge placed
This and the following few sentences are describing a calculus equation using words instead of formulas.
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Energy Stored in Capacitors
This formula, \(E=\frac{1}{2}\frac{1}{C}Q^2\) is actually related to oscillating currents in a circuit, as we shall see in Ch. 23.
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joules
Energy delivered from a defibrillator's cap. E.g., "At 200 J, the ZOLL RBW delivers more average current to high-impedance patients than any other biphasic waveform."
Zoll makes all kinds of defibrillators, rated in Joules.
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beat normally.
aka, sinus rhythm,
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pressbooks.online.ucf.edu pressbooks.online.ucf.edu
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What total capacitances can you make by connecting a and an capacitor together?
Hmmmmmm...This would make a lovely iClicker item.
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Figure 6. A combination of series and parallel
Uh oh
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Suppose you want a capacitor bank with a total capacitance of 0.750 F and you possess numerous 1.50 mF capacitors. What is the smallest number you could hook together to achieve your goal, and how would you connect them?
A brain burner.... work this out before Monday lecture if you can!!!!!!
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Find the total capacitance of the combination of capacitors
First two capacitors are parallels: \(10\mu F\) and \(2.5\mu F\), so they simply add up the preliminary combo capacitance: \(C_{12}=12.5\mu F\). Easy.
However, there is one cap in series with those first two, so now you employ the reciprocals formula for the total equivalent capacitance \(C_{eq}\), viz.
$$\frac{1}{C_{eq}}=\frac{1}{C_{12}}+\frac{1}{0.30\mu F}$$
So the common denominator is semi-nasty, \(cd=\left(12.5\right) \left(0.3\right) \longrightarrow 3.75 \)
The rest is fractions. Don't forget to flip your \(\frac{1}{C_{eq}}\) fraction to get \(C_{eq}\) itself.
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More complicated connections of capacitors can sometimes be combinations of series and parallel
We will get into this kind of brain burner on Monday, plus in a lab this coming week.
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Total capacitance in parallel is simply the sum of the individual capacitances.
Easier
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parallel connection
The top of three capacitors are equivalent to one big plate, and same for the bottoms.
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Entering the given capacitances
must use common denominators!
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for any number of capacitors connected in series.
For \(n\) capacitors in series, $$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\cdots+\frac{1}{C_n}$$
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total voltage is the sum of the individual voltages
...or in Dr. Brueckner's parlance...
$$\Delta V=\frac{Q}{C_{eq}}=\frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3}$$
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voltages across the individual capacitors are
- First capacitor, \(\Delta V_1=\frac{Q}{C_1}\)
- Second capacitor, \(\Delta V_2=\frac{Q}{C_2}\)
- Third capacitor, \(\Delta V_3=\frac{Q}{C_3}\)
Note that the assumed charge load at the top of the first capacitor and at the bottom of the third capacitor are assumed to be the same size, \(\pm Q\). This is an application of the conservation of charge: the number of electrons stolen from the top plate is the same as the load of surplus electrons pushed into the bottom plate.
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An equivalent capacitor
Total voltage drop = \(V\) of the battery! But this time it is split up between three separate capacitors
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Multiple connections of capacitors act like a single equivalent capacitor.
A single equivalent capacitance, \(C_{eq}\)
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Figure 8. Capacitor Lab
Pretty nifty simulation. I tracked the electric field line densities for various dielectrics offered. Have a look at this simulation
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water
First mentioned in Session 8.
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Artist’s conception
Nice
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Typical capacitors range from fractions of a picofarad to millifarads .
Household size units for capacitors. Go into Radio Shack and check them out.
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permittivity
This property, permittivity, is related to a substance's ability to be polarized. You can look up the specs for permittivity for many substances, e.g., for muscle fiber. However, the vacuum also takes a value, denoted \(\epsilon_0\) and used here for parallel plates, even though the vacuum has no substance.
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Since the field lines end on charges in the dielectric, there are fewer of them going from one side of the capacitor to the other.
I detest this description, but it sort of makes some sense.
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more charge
...from the battery
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conduct
Fried dielectric time!
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dielectric constant
Many studies of dielectric properties, biological and otherwise.
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breakdown
Breakdown:
- Sparks if vacuum or air filled capacitor;
- fried dielectric if filled with a dielectric material like paper or paraffin.
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across
For a singly ionized sodium atom, the time to cross this membrane is about \(\Delta t = 0.02\: ns\)... pretty quick!
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membrane
As mentioned in lecture. For those of you studying biology, this is an important application
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thin foils placed close together
This is why the authors show the rolled up capacitor in Fig. 1
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the total number is proportional to the number of charges.
flux concept
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rolled
Can be approximated as parallel plates, with an insulating layer in between.
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store
They also store energy in the electric field. This is the first time we have had something other than a Sir Isaac Newton \(F=ma\) style object with mass that can carry energy.
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A capacitor is a device used to store electric charge.
A great paragraph about what a capacitor is and how it works
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No wonder it took astronomers a long time before they could measure such tiny shifts.
The ancient Greeks could not measure with this precision, nor could the great Tycho Brahe. Kepler and Galileo, Newton and Halley: nope. But by the 1800s, yup, it started becoming possible, with better telescopes and measuring devices.
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In this text, we will use light-years as our unit of distance, but many astronomers still use parsecs when they write technical papers or talk with each other at meetings. To convert between the two distance units, just bear in mind: 1 parsec = 3.26 light-year, and 1 light-year = 0.31 parsec.
This is the end of the material in Ch. 19 needed for Exam 1.
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Back in the days when most of our distances came from parallax measurements, a parsec was a useful unit of distance, but it is not as intuitive as the light-year.
True, but astronomers still use both pc and LY!
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parallax
Parallax angle P, in the diagram
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Bessel made the first authenticated measurement of the distance to a star (61 Cygni) in 1838, a feat that had eluded many dedicated astronomers
Actually, a successful parallax measurement would've satisfied Plato, Aristotle et al., in their day, that Earth orbited the Sun. Unfortunately, they did not have good enough technology. But neither did Kepler and Galileo. Bessel bagged 61 Cygni 200+ years after Galileo.
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Triangulation.
This is essentially what astronomers do when they make pallalax measurements. But for stars, it is a much larger triangle.
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Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.
I like this question. It is not a calculation, but it would be very nice to ask in class.........hmmmmm
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Problems & Exercises
A lot of sketching.... for after Exam 1!!
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The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart.
Very interesting
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One of the most important cases is that of the familiar parallel conducting plates
We talked about this a lot in Session 9.
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the equipotential lines can be drawn simply by making them perpendicular to the electric field lines.
A nice sketching exercise, equipotential lines of a dipole field. We might go through this in our first session after Exam 1.
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Because a conductor is an equipotential, it can replace any equipotential surface. For example, in Figure 1 a charged spherical conductor can replace the point charge, and the electric field and potential surfaces outside of it will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its center.
Huge amount of difficult calculus behind this paragraph, enough to choke Sir Isaac Newton's horse.
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There can be no voltage difference across the surface of a conductor, or charges will flow.
Correct. In a conducting material, the surplus charges will redistribute themselves into dynamic equilibrium, equal distances from each other.
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Work is zero if force is perpendicular to motion.
from PHY2053!!
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electric field lines point radially away from the charge, they are perpendicular to the equipotential lines
True in general for small patches of spacetime, as I mentioned at the end of Session 9.
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Equipotential lines are always perpendicular to electric field lines.
Discussed in Session 9
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Equipotential Lines
Visual way of thinking about the electromagnetic field, and very useful in quantum mechanics.
Does this diagram remind you of a hydrogen atom/Quantum_Mechanics/09._The_Hydrogen_Atom/Bohr's_Hydrogen_Atom)?
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analogous to taking sea level as when considering gravitational potential energy, .
As I mentioned in an earlier annotation.
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Example 2: What Is the Excess Charge on a Van de Graaff Generator
Bypass this example
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Example 1: What Voltage Is Produced by a Small Charge on a Metal Sphere?
Bypass this example
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The potential at infinity is chosen to be zero.
Just as we have the freedom to choose the elevation at which \(GPE=0.0\: J\) in a free fall problem near the surface of Earth: gym floor for a basketball problem, foot of a cliff for a Ferrari driving off a cliff problem, or the top of the same cliff for the Ferrari problem.
NASA will take \(GPE=0.0\: J \text{ as } r \longrightarrow \infty \) since they are ranging way past the surface of Earth and out into space.
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it can be shown that
One of the most annoying phrases in a physics textbook, "it can be shown that..." It is an author's evasive maneuver to avoid pages and pages of nasty calculus equations. Fortunately, that is okay in PHY2054!
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spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge.
Like the top of a Van de Graaff generator
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general relationship between voltage and electric field
Cf., Session 9 in YouTube
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Electron Gun
Yeah, the old timey method for generating a tv picuture, in the old tv tubes you used to see before flat screen technology took over. and The gun is in back, targeted at the front tv screen.
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field creates enough ionization
I.e., ripping outer electrons from \(O_2\), \(N_2\) and \(H_2 O\) molecules, making them into conduction electrons. BANG!
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since points create greater fields than smooth surfaces.
smooth versus sharp surfaces... Notice that insulators on telephone poles are nicely rounded ceramic or glass: and here is a closeup:
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E = V/d.
To encode directionality, should be $$\vec{E}=-\frac{V}{d}$$\ or better yet, $$\vec{E}=-\frac{\Delta V}{\Delta s}$$
...but the authors are only talking about magnitudes here.
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units for electric field are volts per meter.
Include this with my comments on units in Session 9.
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since the path is parallel to the field,
...for this parallel plates example only. In general, one could have any kind of parabolic path between the plates, just as between elevations \(y=0.00\: m\) and \(y=40.0\: m\) from the top of the UCF library to the sidewalk, you could have any number of differing parabolic trajectories for a water balloon, depending on how hard you throw it and in what direction.
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The electric field strength between two parallel conducting plates separated by 4.00 cm is . (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)
This is another nice exercise.
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What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of
Good. I like this basic problem
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two parallel metal plates
Important example
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move 5000 C of charge
What does it mean for a battery to "move 5000 Coulombs"? A battery is rated in Amp hours, e.g.,
An amp hour is a unit of charge: $$1.00\:A \times 1.00\:hour$$ $$1.00 \text{Coulomb}/\text{sec} \times 3600\:sec$$ $$3600 Coulombs$$
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To have a physical quantity that is independent of test charge, we define electric potential
discussed in Session 8
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PE can be found at any point by taking one point as a reference and calculating the work
Similar to the customary approach to GPE in a free fall system. You can define any elevation you like to be the zero point of the potential energy function, $U$... $$U\left(y\right)=-mg\Delta y$$
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the potential energy (because it depends only on position)
A scalar-valued function of position, though a ton of trig is usually encoded in the function
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as if the charge is going down an electrical hill
Emphasis on "as if" !!! ...because of the ambiguity in forces and potential energies that rises from having positive and negative charges
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Electric Potential
Further abstraction. \( \Delta V=-E \Delta x \) in a uniform field \(E\), e.g., between parallel charged plates. Does that formula remind you of the work formula?
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A motorcycle battery, for example, is small and would not be very successful in replacing the much larger car battery, yet each has the same voltage.
Each has the same voltage -- determined by the cource charge array, not the apparatus (motorcycle vs. car)
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ions cross cell membranes
ionic pumps
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Two equivalent representations of the electric field
Reviewed in Session 8
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Sketch the electric field lines in the vicinity of two opposite charges, where the negative charge is three times greater in magnitude than the positive.
BANG! Another exercise I like.
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Figure 8 shows the electric field lines near two charges and . What is the ratio of their magnitudes?
Yes, I like this exercise, too.
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1: (a) Sketch the electric field lines near a point charge . (b) Do the same for a point charge
I like this exercise
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Field lines can never cross
Another flux law
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The direction of the electric field is tangent to the field line at any point in space
Useful for visually interpreting the curvature of field lines.
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The strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area perpendicular to the lines
also a flux law
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not a physical entity in themselves
Although Michael Faraday at first DID think that field lines were physical. He called them lines of force.
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The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge
A flux law. If we were using calculus, there would be a huge calculus equation for this law, but the verbal form here is perfectly righteous and useful.
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A certain five cent coin contains 5.00 g of nickel. What fraction of the nickel atoms’ electrons, removed and placed 1.00 m above it, would support the weight of this coin? The atomic mass of nickel is 58.7, and each nickel atom contains 28 electrons and 28 protons.
OH MY GOODNESS!
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At what distance is the electrostatic force between two protons equal to the weight of one proton?
A brain burner!!!
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How do you split the charge to achieve the greatest force?
Not sure what this is asking. BYPASS
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A test charge of is placed halfway between a charge of and another of separated by 10 cm. (a) What is the magnitude of the force on the test charge? (b) What is the direction of this force (away from or toward the charge)?
We worked on similar calculations in class.
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f two equal charges each of 1 C each are separated in air by a distance of 1 km, what is the magnitude of the force acting between them? You will see that even at a distance as large as 1 km, the repulsive force is substantial because 1 C is a very significant amount of charge.
Fairly easy to calculate, if you know the value of Coulomb's constant, \(k\)
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How far apart must two point charges of 75.0 nC (typical of static electricity) be to have a force of 1.00 N between them?
I like this one, a good basic workout.
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distance between two objects squared to an accuracy of 1 part in .
Theoretically, an inverse r<sup>2</sup> force has infinite range. So: gravitation and electromagnetism.
Caveat: electromagnetic interactions can be screened, like losing your cell phone signal inside certain buildings on campus.
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Coulomb’s law
We reviewed this in Session 5, 09/06
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How many electrons does it have?
Nice exercise, relating the metric unit of charge, the Coulomb, to the fundamental charge,
e=1.602 x 10<sup>-19</sup> Coulomb
Hint: if its net charge is negative, then it has EXTRA electrons.
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A 50.0 g ball of copper has a net charge of . What fraction of the copper’s electrons has been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)
A brain burner!
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When a glass rod is rubbed with silk, it becomes positive and the silk becomes negative—yet both attract dust. Does the dust have a third type of charge that is attracted to both positive and negative? Explain.
I like this question.
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attraction of water to the charged rod
I like this exercise. It is a cool demonstration you can do at home!
- Turn on the water to the lowest setting at which water streams out without forming droplets;
- charge up a plastic comb by scuffling it on your shirt;
- ease the comb in close to the vertical stream of water...
...How do you explain the fact that the stream dips slightly toward the comb (as in the photo) and never away from the comb?
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The same effect
The electrons at the left hand side of the grey conducting block flee the copper colored rod, which is net negative. Those fugitive electrons head over to the right hand side of the conducting block. POLARIZED!
This is basically what happened with the soda pop can demonstration.
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allowing electrons to be attracted from the earth’s ample supply
Earth is negatory
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Charging by induction.
polarize, then separate
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the leaves
positive charges "move" to the sharpest topography of the device, just as they move to a students hair when touching the Van de Graaff generator.
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Some of the electrons
e.g., some of the valence electrons
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salty water
...as opposed to pure water, no dissolved minerals, which is actually a fair insulator.
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The Van de Graaff Generator
Demonstrations in Session 7, Sept. 11
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hair
very "sharp" compared to other parts of the body
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Excess charge on a nonuniform conductor becomes most concentrated at the location of greatest curvature.
We mentioned this in Session 7
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surrounding material
i.e., air
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close together
Plate width \(W\gg d\) the distance between plates. Normal batteries and capacitors rely on this limit.
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Properties
More statements based on flux.
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The mutual repulsion of excess positive charges on a spherical conductor distributes them uniformly on its surface. The resulting electric field is perpendicular to the surface and zero inside. Outside the conductor, the field is identical to that of a point charge at the center equal to the excess charge.
Yes, important when applied to wires in a circuit.
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A conductor placed in an electric field will be polarized.
This is why the aluminum soda pop can rolled in Session 7 demonstration
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Water is a strongly polar molecule.
Here is a better model than Fig. 2 <script async src="//embedr.flickr.com/assets/client-code.js" charset="utf-8"></script>
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The movement of these ions through cell membranes is crucial to the motion of nerve impulses through nerve axons.
Membranes and batteries and capacitors have similar structure.
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bonds
hydrogen bonds
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it is the electrostatic force that not only holds the molecule together but gives the molecule structure and strength.
Mentioned in terms of complex organization, Session 7.
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With the vector pointing rightward, it is effectively pointing at the center of the Nardo Ring — it is centripetal.
This statement and surrounding statements mentioned in HW 03.
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This electric field strength is the same at any point 5.00 mm away from the charge that creates the field.
Spherical symmetry, very handy, though lots of trig is possible. All complicated fields, like the electric field of a charged metal plate in a battery, is built up of zillions of point charge fields (using calculus and trig for days).
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The electric field is defined in such a manner that it represents only the charge creating it and is unique at every point in space.
Very important. This cannot be done with forces. Cf., Session 7
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strands of hair to repel
Again, the conundrum of hands touching the generator but the strands of hair displaying the electrical effect.
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observed charges
The author is being tricky here. QUarks are subatomic particles with partial charges, The up quark (u) has charge $$+\frac{2}{3}e$$ and the down quark (2) has fractional charge \(-\frac{1}{3}e\)
- neutron = dud
- proton = uud
However, quarks are hard to pull out of a proton or neutron and have never been observed in isolation. *
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Similarly, electrons have a combined charge of −1.00 coulomb.
$$6.25\times 10^{18}\text{ electrons}\longrightarrow -1.00\:Coulomb$$
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cosmic rays
E.g., muons that form from cosmic rays.
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in equal amounts
i.e., neutral atoms, not ions
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explore the nature of the force between charges.
The electromagnetic interaction is trickier than the gravitational interaction, because
- there are two kinds of charge, and
- there is repulsion as well as attraction.
For this reason, deciding the net electrical force on an electron or a proton, or an array of electrons or an array of protons, can be inticate, accounting-wise, because you have to account for
- the geometry of the array,
- the sign of the charges, and
- the repulsion or attraction of the charges on each other
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amber
The Greek word for amber is ήλεκτρο, from which we get the word electric, electron etc.
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the weak nuclear force
Actually, we now have a great unifying theory for electromagnetic and weak nuclear interactions. It is called "electroweak theory." We won't be studying it, but it is out there. Here is something from Georgia State Hyperphysics You can take a peek at it, read around if it strikes your fancy.
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The sliding motion stripped electrons away from the child’s body, leaving an excess of positive charges, which repel each other along each strand of hair.
If the sliding motion is the seat of this little kid's pant, then why do excess positive charges end up along each strand of hair?
We will understand this conundrum directly.
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Stardust sample return mission
Very important investigation for us, the Stardust Mission.
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Chemical Condensation Sequence in the Solar Nebula.
This diagram was first mentioned in the Getting Started Fall 2019 video in YouTube!
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Figure 2. (a) We analyze two-dimensional projectile motion
Sneak preview on syllabus is related to this analysis. Study both. Acceleration
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Comets generally have orbits of larger size and greater eccentricity
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They are about the same to the nearest power of 10.
This is a horrible sentence.
When a scientist deals with huge numbers, as in astronomy, it is sometimes "close enough" if they have the same power of 10 in scientific notation.
- Mars polar cap \(= 1.00 \times 10^{15}\, \text{tons}\)
- Greenland ice cap \(2.85 \times 10^{15}\, \text{tons}\)
So a better sentence would be this: \(\text{\color{blue}The mass of frozen water in the Mars polar cap }\)\(\text{\color{blue}is of the same order as the Greenland ice cap}.\)
One commonly hears egghead scientists saying that two quantities "are about the same order," and by that they mean the two quantities are righteous and equivalent.
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The rovers (Spirit, Opportunity, and Curiosity)
Small but mighty, the good and faithful rovers that have sent us so much data about Mars.
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Future missions will include the return of martian samples
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The seasonal caps on Mars are composed not of ordinary snow but of frozen CO2 (dry ice).
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polar cap area
Using \(\pi r^2\) for the area here is an underestimation, because \(\pi r^2\) is good for a flat circle, but the polar cap is not flat! It is curvature.
However, using \(\pi r^2\) is
- easy
- and close enough
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The ratio of the distance between the foci to the length of the major axis is called the eccentricity of the ellipse.
$$e=\sqrt{1-\frac{b^2}{a^2}}$$
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behavior of planets based on their paths through space.
"...based on their paths." This is bass ackward relative to, e.g., Ptolemy. For Ptolemy, he based everything on circles and forced everything into a complex system involving epicycles, deferents, equants etc. To some degree, Copernicus and Galileo were also stuck thinking "circles." Kepler, however, took the path that Nature showed him in Tycho's measurements -- especially Mars' ellipse -- and then figured out a pattern from that. And he figured out three patterns, actually.
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Kepler Helps Weigh the Galaxy
As previously stated, Kepler's Third Law is EVERYWHERE!!!!
: )
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In science, what seems to be a reasonable assumption can later turn out to be wrong
Scientists must always be humble about their findings
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objects orbiting at large distances from a massive object will move more slowly than objects that are closer to that central mass.
E.g., a comet really moving fast at perihelion and slowing down at aphelion. E.g., Uranus and Neptune. Nearly the same mass, but orbital semimajor axes 19.2 AU for Uranus and 30 AU for Neptune; their orbital "years" are 84 years for Uranus but 164 years for Neptune.
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the nearer a planet is to the Sun, the greater its orbital speed.
Sir Isaac Newton figured out why this is true, in his theory of universal gravitation -- which is a few chapters ahead.
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We can use Kepler’s law (see Orbits and Gravity) and our knowledge of the visible star to measure the mass of the invisible member of the pair.
One short sentence, but powerful. Thank you, Professor Kepler!
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Calculating the Effects of Gravity
Bypass this calculation until end of the semester.
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Heat escaping from the interior provides energy for the formation of our planet’s mountains, valleys, volcanoes, and even the continents and ocean basins themselves.
Main source of forces and motion = convection. Huge blobs of molten lava convect from core to surface, like water boiling in a pot on the stove or a thunderstorm convecting water vapor and liquid water in the atmosphere.
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