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REVIEW FOR FINAL EXAM December 2009

BASIC PHYSICS 218 COULOMB’S LAW

ELECTRIC FIELD

ELECTRIC FIELD LINES

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Consider a ring of uniform charge

Find Ex at P

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Where

Etc.

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GAUSS’S LAW and ELECTRIC FLUX

Example 22.9 Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R. a. Find the electric field at point p where r < R.

b. Find the electric field at point p where r > R.

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ELECTRIC POTENTIAL

ELECTRICAL POTENTIAL IS POTENTIAL ENERGY PER UNIT CHARGE

POTENTIAL DIFFERENCE

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Gauss’s Law

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Choose where

Example 23.11 Potential on axis of ring of charge.

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Find potential at P

ELECTRON VOLT An electron volt is a unit for energy. It is the work necessary to move an electron (charge ) a potential difference of 1 volt.

Capacitors

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Parallel plate capacitors

But

C = ?

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Need

Gauss’s Law gives

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CAPACITORS IN CIRCUITS

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ENERGY IN CAPACITOR AND ELECTRIC FIELD

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Use definition of capacitance

Or

Energy density

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Therefore

DIELECTRICS Add material between plates and C increases.

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Current is the time rate of passage of the charge.

RESISTIVITY of a material RESISTANCE of an object

This is Ohm’s Law.

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A copper rod with cross section A has a length L what is its resistance? Work for and . Resistivity of Cu Therefore

If have I and R will have power lost.

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Circuit elements:

Other symbols

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Consider the following circuit.

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What is the current through the 6 Ω resistor?

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KIRCHHOFF’S RULES Junction Rule The sum of the currents into a junction is zero.

Loop Rule The sum of the potential differences in a loop is zero.

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R-C CIRCUITS

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Discharge C through R

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MAGNETIC FIELD AND MAGNETIC FORCES

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MAGNETIC FLUX Just like Electric Flux but with magnetic field.

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MAGNETIC FIELD NEAR WIRE CARRYING CURRENT.

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Magnet Field from wire carrying current.

Again is a unit vector. This equation is the Biot-Savart Law.

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This is Ampere’s Law

Find the Magnetic Field inside (r < R) of a conducting cylinder.

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r

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What is B in solenoid? (Use Ampere’s Law)

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Magnetic Flux

If this flux changes an emf will be induced in the area.

Faraday’s Law

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Lenz’s Law – direction of emf

The direction of the induced emf is such that it tends to produce a current that will create a magnetic flux to oppose the change in magnetic flux through the loop.

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If is 1.0 A/s what is the emf in the loop?

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Motional emf

Dx

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Mutual Inductance I1 #1 #2

I2

Then

is the Mutual Inductance

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Faraday’s Law gives

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Self Inductance

Thus

Faraday’s Law

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Self-Induced emf

What is the inductance, , of the black coil?

Area A

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B

Ampere’s Law

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Magnetic Field Energy Consider the coil

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What is stored energy in the black solenoid?

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Put into equation for

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Energy density

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R-L Circuit

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Energy propagating with an EM Wave We define a vector, the Poynting vector, to be

The direction of the Poynting vector is the direction of propagation of the wave. The magnitude of the Poynting vector is the energy per unit time per unit area (power per unit area) delivered by the wave.