Magnetic Induction

Physics 72 Bareza AY 15-16 1st sem 2

If the magnetic flux through a circuit changes,

an emf and a current are induced in the circuit.

Electromagnetic Induction

A time-varying magnetic field can act as a source of electric field.

A time-varying electric field can act as a source of magnetic field.

Maxwell’s equations.

Chapter 29

Magnetic Induction

29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields


Objective

• Identify the factors that affect the magnitude of the induced EMF and the magnitude and direction of the induced

current



We connect a coil of wire to a galvanometer, then place the

coil between the poles of an electromagnet whose magnetic

field we can vary. Here’s what we observe:

When there is no current in the

electromagnet, so that B = 0, the

galvanometer shows no current.

When the electromagnet is turned on,

there is a momentary current through the

meter as B increases.

When B levels off at a steady value, the

current drops to zero, no matter how

large B is.


With the coil in a horizontal plane, we squeeze

it so as to decrease the cross-sectional area

of the coil. The meter detects current only

during the deformation, not before or after.

When we increase the area to return the coil to

its original shape, there is current in the

opposite direction, but only while the area of the

coil is changing.

If we rotate the coil a few degrees about a

horizontal, the meter detects current during the

rotation, in the same direction as when we

decreased the area. When we rotate the coil

back, there is a current in the opposite direction

during this rotation.


If we jerk the coil out of the magnetic field, there

is a current during the motion, in the same

direction as when we decreased the area.

If we decrease the number of turns in the coil by

unwinding one or more turns, there is a current

during the unwinding, in the same direction as

when we decreased the area. If we wind more

turns onto the coil, there is a current in the

opposite direction during the winding.


When the magnet is turned off, there is a

momentary current in the direction opposite

to the current when it was turned on.

The faster we carry out any of these

changes, the greater the current.


If all these experiments are repeated with a

coil that has the same shape but different

material and different resistance, the

current in each case is inversely

proportional to the total circuit

resistance. This shows that the induced

emfs that are causing the current do not

depend on the material of the coil but

only on its shape and the magnetic field.


The common element in all

these experiments is

changing magnetic flux

through the coil

connected to the

galvanometer.


Different ways for induction:(1) Changing magnetic field strength

(2) Changing Area

(3) Changing relative orientation between

magnetic field and area vector

*with the condition that magnetic field and

area vector is not completely perpendicular

for (1) and (2)

Chapter 29

Magnetic Induction



Objective

• Calculate the induced EMF in a closed loop due to a time-varying magnetic flux using Faraday’s Law

’


’


Faraday's law of induction

The induced emf in a closed loop equals the

negative of the time rate of change of magnetic

flux through the loop.

’


Magnetic Flux

Magnetic Flux thru an open surface

If is uniform, then

’


Direction of the induced emf

’


Direction of the induced emf

’


If we have a coil with N identical turns, the total emf

in a coil with N turns is

Magnetic flux through a single coil

Where:

’


The figure shows a wire coil being

squeezed in a uniform magnetic field.

While the coil is being squeezed, is

the induced emf in the coil

A. clockwise,

B. counterclockwise, or

C. zero?

Once the coil has reached its final

squeezed shape, is the induced emf

in the coil

A. clockwise,

B. counterclockwise, or

C. zero?

Example:

’


Example:

Answers:(a) emf = 0.0900*0.190 V(b) I = 0.0900*0.190/0.600 A

’


Example:

’


Seatwork:A conducting loop is placed perpendicular to a constant

uniform magnetic field as shown. If the area of the loop

increases at a rate α, find the following.

a) Induced emf ε

b) Direction of induced current

(Answer: ε = -Bα, |ε| = Bα)

(Answer: CW)

Chapter 29

Magnetic Induction



Objective

• Describe the direction of the induced electric field, magnetic field and current on a conducting/non-conducting

loop using Lenz’s Law

’


’


Lenz’s Law

The direction of any magnetic induction effect is

such as to oppose the cause of the effect.

The induced emf and induced current are in

such a direction as to oppose the change

that produces them.

It gives only the direction of induced emf and current.

’


Lenz’s Law

’


Recall:

’


Recall:

Example:

’


Explanation: Through RHR, B due to I inside coil is out of the page. The B strength decreases through time since B is proportional to I due to wire. B induced on coil is out of the page due to decreasing B strength via Lenz’s law.Answer: current is CCW using RHR.

’


Example:Answers:(a) CCW(b) CW(c) none

’


IP

Seatwork:A very long wire is part of a circuit with

a switch. Beside it is a conducting loop.

The switch, initially open, was closed

causing a current to flow. During the

switching, what is

a) the direction of the induced magnetic

field inside the coil?

b) the direction of the induced current

through point P?

Out of the page

Downward

Chapter 29

Magnetic Induction



Objective

• Given the velocity and the orientation of a conductor in a uniform magnetic field, determine the induced EMF, electric

field, magnetic field and current



We can gain additional insight into the origin of the

induced emf by considering the magnetic forces on

mobile charges in the conductor.

If a conductor moves in a magnetic field, a motional emf is induced.



The moving rod has become a

source of electromotive force.

motional electromotive force

(length and velocity perpendicular to

uniform magnetic field)


motional electromotive force

If the total circuit resistance of the U-shaped

conductor and the sliding rod is R,

the induced current I in the circuit is given


In general,

More useful in solving problems involving moving conductors!

Applicable only for moving conductors in constant magnetic field

For any conductor with any shape in a uniform or non-uniform magnetic field

For a closed conducting loop

This is always true.

These are the same!


Example:

It requires large velocity to achieve 1.5 V which is still a small voltage so not really.


Example: Answer:(a) emf = 1.5*0.75*5.0(b) All CCW(c) I = 1.5*0.75*5.0/25.0


Seatwork:

Answers:(a) b(b) b(c) None(d) Along direction of -53 deg

ANNOUNCEMENT

• Arrive exactly at 7AM on ThursdayWarning: Recit is relatively longer than your previous ones. This will test your time-budgeting skill. [Coverage: from 29-1 to 29-4]

• Be present on Thursday since take home recit will also be distributed. [Coverage: 29-5 and previous lessons]

Chapter 29

Magnetic Induction



Objective

• Compare and contrast, electrostatic field and non-electrostatic/induced electric field




Question:What force makes the charges move around the loop?

There has to be an induced electric field in the

conductor caused by the changing magnetic flux

(magnetic field).

Recall:


Work done by the induced electric field per unit charge

Induced electric field is not conservative.

Also,

Valid only when integration path is stationary.



Induced Electric Field


A circular conducting loop is immersed in a spatially uniform

magnetic field that is decreasing at a constant rate. Which

of the following best describes the electric field induced in

the loop?

A. Constant and non-conservative

B. Decreasing and non-conservative

C. Increasing and non-conservative

D. Constant and conservative

E. Decreasing and conservative

Example:

In which time interval is the value of the induced

electric field largest for a solenoid with n turns

per meter and radius R at a distance r (r < R) from

the axis of the solenoid?

Seatwork:


ANNOUNCEMENT

• Arrive exactly at 7AM tomorrowWarning: Recit is relatively longer than your previous ones. This will test your time-budgeting skill. [Coverage: from 29-1 to 29-4]

• Be present tomorrow since take home recit will also be distributed. [Coverage: 29-5 and previous lessons]

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Magnetic Induction

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