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Chapter 30: Induction and Inductance

Introduction

What are we going to talk about in chapter 31:

• A change of magnetic flux through a conducting loop produces a current!

• What is lenz’s law?

• What is the relation between induction and energy transfer?

• What are eddy currents?

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30-2: Two symmetric situations

YES!! This is formulated in Faraday’s law.

It is the basis for the electric generator!!

We have seen (ch. 29) that: Current loop in a magnetic field leads to torque (the basis for the electric motor).

Is the opposite also true?

Does a torque on a loop in a magnetic field lead to a current?

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30-2: Two experiments:

Experiment #1: Loop of wire connected to a galvanometer. A magnet is moved towards or away from the loop.

Result: an induced current is set up in the circuit as long as there is relative motion between the magnet and the coil (w/o a battery!!). The work per unit charged to produce the current is called the induced emf.

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Experiment #2: Primary circuit has an emf, secondary circuit has no emf.

Result: an induced emf (and current) is produced in the secondary circuit only when the current (and hence the magnetic flux) is changing.

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30-3: Faraday’s law of induction

E = - dB/dt

where B is the magnetic flux through the circuit.

The emf induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit.

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What factors effect the emf?

• The magnitude of B may vary with time

• The area of the circuit can change with time

• The angle () between B and the plane can change

• A combination of the above

Checkpoint #1

If there are N loops, all of the same area:

E = - N dB/dt

where B is the magnetic flux through one loop circuit.

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Some applications:

• Cooking utensils

• Ground fault interrupter (GFI)

• Microphone (or electronic guitar!!)

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Ans. 4.05 V, 2.03 A.

Example: A coil is wrapped with 200 turns of wire on the perimeter of a square frame of side 18 cm. The total resistance of the coil is 2W. B is the plane of the coil and changes linearly from 0 to 0.5 T in 0.80 seconds. Find the emf in the coil while the field is changing. What is the induced current?

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30.4: Lenz’s law:

Lenz’s law says: The polarity 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.

For example: What is the direction of the induced current in the figure? Why?

The current is clockwise.

What happens if you stop?

What happens if you reverse direction?

10Checkpoint #2

Another example: a bar magnet is moved to the left/ right toward a stationary loop of wire.

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30.5: Induction and energy transfers

q E = q v B

Consider a straight conductor (length l) moving with constant velocity (v to the right) in a perpendicular magnetic field (B into the page).

Electrons will move towards the bottom and accumulate there leaving a net positive charge at the top until:

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Notice that:

B = B l x

Therefore, a potential difference V will be created across the conductor:

V = E l = B l v

The upper end is at higher potential.

Which end is at a higher potential?

If the direction of motion is reversed, the polarity of V is also reversed.

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Therefore, the induced emf E is:

E = -d B/dt = - B l v

The induced current is:

i = B l v/R

This power is dissipated in the resistor (i2 R)!!

The power (P) delivered by the applied force is (from phys-101):

P = Fappv = i l B v = (Blv)2/R =E2/R

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The power applied:

Papp = F v

The induced emf:

E = - dB/dt = B l v

i = B l v/R

If there is a rectangular circuit part of which is in perpendicular magnetic field and is being pulled out of the field, you must apply a constant force (F) in order for the circuit to move with constant speed (v).

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Therefore, the force exerted on the wire is:

F = i l B = B2 l2 v/R

The power delivered/ applied due to the wire is:

Papp = B2 l2 v2/R

But, the power dissipated is:

Pdiss = i2 R = B2 l2 v2/R

Therefore,

Pdiss = Papp

That is, the work you do in pulling the loop through the magnetic field appears as thermal energy in the loop!

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Eddy currents:

Checkpoint #3

رب لله الحمد أن دعوانا آخر والعالمين