32N 29 Electromagnetic Induction

Electromagnetic

Induction

29 - Electromagnetic Induction 1Arlyn D. Macasero-Roque

We have learned that if we put a

current-carrying loop in a magnetic

field, magnetic forces create a torque

to turn it.





to turn it.

What will happen if we switch the

current off and turn the loop by hand?

Will the opposite occur, that is, will a

current appear in the loop?





to turn it.

What will happen if we switch the

current off and turn the loop by hand?

Will the opposite occur, that is, will a

current appear in the loop?

Yes. This is called

Faradays law of induction.

Magnetic torque is the basis for the electric motor and Faradays law is the basis for the electric generator.


29.1 Induction Experiments

Faradays First Experiment

If a magnet is moved toward a closed loop of wire, current is induced in

the wire. As the magnet is withdrawn, current is again induced. The

direction of the current is reversed when the direction of motion is

reversed.



Faradays First Experiment

If a magnet is moved toward a closed loop of wire, current is induced in

the wire. As the magnet is withdrawn, current is again induced. The

direction of the current is reversed when the direction of motion is

reversed.

1. A current appears only if there is relative

motion between the magnet and the loop;

the current disappears when relative motion

stops.

2. Faster motion produces a greater current.

3. Moving the magnets north pole toward the

loop causes clockwise current, then moving

the north pole away causes counter-

clockwise direction of current. South pole

movements produce opposite directions.



Faradays 2nd Experiment

If two loops of wire are close together and a changing current is produced

in one loop, then current is induced in the second loop.

Current in second loop is observed ONLY when current in the first

loop is changing.


If the switch is closed to

switch on the current in the

first loop, the galvanometer

needle deflects and

registers the current in the

second loop after which, it

goes back to zero. When the

switch is opened, the needle

of the galvanometer deflects

in the opposite direction and

then returns to a zero

reading.

29.2 Faradays Law


The magnitude of the induced emf e in a conducting loop is equal to

the rate of change of the magnetic flux through the loop:

The negative sign indicates that the induced emf tends to oppose

the change in magnetic flux.

Bd

dte

29.2 Faradays Law


The magnitude of the induced emf e in a conducting loop is equal to

the rate of change of the magnetic flux through the loop:

The negative sign indicates that the induced emf tends to oppose

the change in magnetic flux.

Bd

dte

If the coil consists of N turns, the total induced emf is

BdNdt

e

29.2 Faradays Law


( cos )Bd d BAN Ndt dt

e

We can change the magnetic flux through a coil in 3 ways:

1. Change the magnitude of the magnetic field B within the coil

2. Change the area of the coil A within magnetic field

3. Change the angle between the magnetic field and the areavector of the coil.

Check your Understanding

An electromagnet generates a magnetic field with field lines

passing through the coil as shown. What is the direction of

the induced emf in the coil if the field

(a) points to the right and is increasing?

(b) points to the right and is decreasing?

(c) points to the left and increasing?

(d) points to the left and decreasing?

(e) is unchanged?



An electromagnet generates a magnetic field with field lines

passing through the coil as shown. What is the direction of

the induced emf in the coil if the field

(a) points to the right and is increasing?

(b) points to the right and is decreasing?

(c) points to the left and increasing?

(d) points to the left and decreasing?

(e) is unchanged?


2 to 1

1 to 2

1 to 2

2 to 1

zero

A single loop of wire has an area of 0.090 m2 and is in a region ofuniform magnetic field directed 30 from the plane of the loop. Themagnetic field is initially 3.8 T and is decreasing at a constant rate of0.19 T/s.

(a) What is the magnitude of the induced emf in the loop?

(b) If the loop has a resistance of 0.30 W, what is the magnitude of theinduced current in the loop?



A single loop of wire has an area of 0.090 m2 and is in a region ofuniform magnetic field directed 30 from the plane of the loop. Themagnetic field is initially 3.8 T and is decreasing at a constant rate of0.19 T/s.

(a) What is the magnitude of the induced emf in the loop?

(b) If the loop has a resistance of 0.30 W, what is the magnitude of theinduced current in the loop?

2

( cos )cos

(0.090 m )(cos60 )(0.19 T/s)

8.6 mV

Bd d BA dBAdt dt dt

e

e

38.6 10 V28.5 mA

0.30 i

R

e

W



The long solenoid S shown (in cross section) in the figure has 22,000turns/m and initially carries a current i = 1.5 A. At its center is placed a130-turn closely packed coil C with 5.0-W resistance and with a diameter of2.1 cm. The current in the solenoid decreases to zero at a steady rate in25 ms. What is the magnitude of the induced emf and induced current incoil C as the current in the solenoid is changing?



The long solenoid S shown (in cross section) in the figure has 22,000turns/m and initially carries a current i = 1.5 A. At its center is placed a130-turn closely packed coil C with 5.0-W resistance and with a diameter of2.1 cm. The current in the solenoid decreases to zero at a steady rate in25 ms. What is the magnitude of the induced emf and induced current incoil C as the current in the solenoid is changing?

Magnitude of induced EMF:

Induced current:

cos0CBC C C C C

d BAd dBN N N A

dt dt dte

0

3 2 7 3

3

(0 1.5)(130 turns) (10.5 10 m) (4 10 T m/A)(22 10 turns/m)

25 10 s

71.3 mV

C C C S

C

diN A n

dte

e

371.3 10 V

14.3 mA5.0

CCi

R

e

W



The figure shows a slidewire generatorcomposed of a U-shaped conductor ina uniform magnetic field perpendicularto the plane of the conductor withmagnitude B = 0.60 T. A 0.10m longmetal rod is laid across the arms of theconductor forming a closed loop with atotal resistance of 0.030 W. If the rodmoves at a constant speed of 2.5 m/s,find the magnitudes of the inducedemf, induced current, and the forceacting on the rod.



The figure shows a slidewire generatorcomposed of a U-shaped conductor ina uniform magnetic field perpendicularto the plane of the conductor withmagnitude B = 0.60 T. A 0.10m longmetal rod is laid across the arms of theconductor forming a closed loop with atotal resistance of 0.030 W. If the rodmoves at a constant speed of 2.5 m/s,find the magnitudes of the inducedemf, induced current, and the forceacting on the rod.

( )(0.6)(0.1)(2.5) 0.15 VB

d d BLx dxBL BLv

dt dt dte

0.155.0 A

0.03i

R

e (5.0)(0.1)(0.6) 0.30 NF iLB



An induced current has a direction such that the magnetic

field due to the current opposes the change in the magnetic

flux that induces the current.


29.3 Lenzs Law


29.3 Lenzs Law



A constant magnetic field exists ina rectangular region of spacedirected into the page. Outsidethis region there is no magneticfield.

A conducting ring slides throughthe region at constant speed,from position 1 to position 5.

For each of the five positions,determine whether an inducedcurrent exists in the ring and, ifso, find its direction.

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32N 29 Electromagnetic Induction