Physics II PHY 202/222

Magnetism

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Magnetism– Test 5Beiser Chapters 27

MC: odd, SP: 5 – 17 odd

Beiser Chapters 28

MC: odd, SP: 1 – 19 odd

Beiser Chapters 29

SP: 3Browne Chapter 26-29 for PHY 222 Students

26: 1,5,9

27: 2,

28: 7

29: 1, 2

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Chapter 27 – Magnetism

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Magnets

When we think of magnets we either consider permanent magnets or magnetic effects of moving charge. Since permanent magnets come from moving charge, we consider moving charge first.

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Magnetic Fields

Unit of magnetic field is the Tesla where

1 T = 1 N/Am = 1 Weber/m2 = 10,000 Gauss

The field around a strong permanent magnet is 0.1 T. An MRI is from 0.2 to 1.5 T. A junkyard electromagnet for lifting cars is 1 T.

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Magnetic Field of a Straight Current

6

IB

2 s

where 1.257 10 Tm / A

Every current in a wire generates a magnetic field.

Point the thumb of your right hand in the direction of the current, and your curled fingers will point in the direction of the field.

The magnitude at a distance s from the wire is given by the formula:

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Magnetic Field of a LoopA current in a loop of wire generates a magnetic field.

Point the fingers of your right hand in the direction of the current, and your thumb will point in the direction of the field inside the coil.

The magnitude of the field inside the loop is given by the formula:

IB single loop

2rNI

B many loopsL

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Earth Magnetism

The Earth has a magnetic field due to currents of molten material in the core.

The magnitude is around

3 x 10 -5 T

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Magnetic Force on a Moving Charge

A charge Q moving in a magnetic field B with velocity v will experience force F.

In the picture, the charge is moving to the right in a magnetic field into the screen. The magnitude of the force is given by

The force will be upwards as follows:

Put the thumb of your right hand in the direction of v. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers for a positve charge, and opposite for a negative charge.

v

Magnetic field into screen

F

B

+QF QvBsin

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Magnetic Force on a Current

F = I L B

v

Magnetic field into screen

F

B

Wire

+Q

I

L – Length of wire in magnetic field

The force will be upwards as follows:Put the thumb of your right hand in the direction of I. Put your fingers in the direction of B. Curl fingers up. Force will be in direction of fingers.

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Force Between two Currents

o 1 2I IF

L 2 s

L

s

If currents are in opposite directions, the force is repulsive; same attractive.

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Ferromagnetism

27.6

27.10

27.12

27.14

27.16

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Chapter 28 – Electromagnetic Induction

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Electromagnetic Induction

A current is produced if:

•If a conductor is moved in a magnetic field

•If a magnet is moved near a wire, especially a coil of wire

•A magnetic field changes near a conductor/coil.

Induced EMF V Blv For a straight conductor moving perpendicular to a magnetic field.

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Faraday’s Law

BAInduced EMF V N N

t t

For a magnet moving in a coil:

Lenz’s Law: an induced current is always in the direction so that it’s own magnetic field opposes the effect that created it.

Hence the negative sign above.

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Transformers

1 1 1 2

2 2 2 1

V N I N

V N I N

N1 N2

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Self Induction

ISelf Induced EMF V L

t

A change in current in a conductor causes a change in magnetic field.

A change in magnetic field causes an self-induced emf.

Where L is the inductance of the circuit component.

For a solenoid:

2N AL

Inductors in Combination

1 2 3

1 2 3

L L L L ... inductors in series

1 1 1 1... inductors in parallel

L L L L

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Energy of an Inductor

21W LI

2

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Time Constants and Current

When a switch in an inductive circuit is closed, the current builds up to it’s full value according to the formula:

t / T0I I 1 e Where the time constant, T = L / R.

28.4

28.6

28.8

28.10

28.12

28.14

28.16

28.18

28.20

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Chapter 29 – Alternating Current Circuits

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Alternating Current

DC Direct Current

V = constant

AC Alternating Current

V = Vmax sin ωt

I= Imax sin ωt

Generators

Generator: Move the coil, electricity out. Motor: Electricity in, motion out.

Split ring commutator

Slip rings

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Effective Values

Since the average AC voltage V = Vmax sin ωt is zero, we need a way to be able to calculate its capacity to do work. So we use the “effective value” or root-mean-square (rms) value.

maxeff max

maxeff max

VV .707 V

2I

I .707 I2

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Phase Angle

ELI – ICEIn an AC circuit with only an inductor (L) the voltage (E) leads the (I) current by 900.

In an AC circuit with only an capacitor (C) the current (I) leads the voltage (E) by 900.

In AC circuits with both inductors and capacitors you would have to find the phase angle as shown in the book.

Maxwell’s Equations

0

B

E0 0 0

QE dA

B dA 0

dE ds

dtd

B ds Idt

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Gauss’s Law for electricity: Electric fields come from charges

Gauss’s Law for Magnetism: There are no magnetic charges/monopoles. Any “ball” has the same B out as in: sum =0

Faraday’s Law: Change in magnetic field makes electricity.

Ampere’s Law: Change in electric field makes magnetism.

ΔE → ΔB → ΔE → … propagates through space as light or other EM waves. WOW!