Faraday’s Law

• Sections 23-1 -- 23-4

Physics 1161: Lecture 14

Changing Magnetic Fields create Electric Fields

Faraday’s Law

• Key to EVERYTHING in E+M– Generating electricity– Microphones, Speakers and MP3 Players– Amplifiers– Computer disks and card readers– Ground Fault Interrupters

• Changing B creates new E

Magnetic FluxcosB BA

Faraday’s Law for Coil of N TurnsBN

t

2:units Tesla m Weber Wb

Lenz’s LawInduced current is in a direction so that it opposes the change that produces it.

Faraday’s Law (EMF Magnitude)

Emf = Change in magnetic Flux/Time

if

if

ttt

Since = B A cos(3 things can change

Faraday’s Law (EMF Magnitude)

Emf = Change in magnetic Flux/Time

if

if

ttt

Since = B A cos(3 things can change

1. Area of loop2. Magnetic field B3. Angle between A and B

Lenz’s Law (EMF Direction)Emf opposes change in flux

• If flux increases: New EMF makes new field opposite to the

original field (to oppose the increase)• If flux decreases:

New EMF makes new field in the same direction as the original field (to oppose the decrease)

Motional EMF circuit

• Direction of Current

• Direction of force (F=ILB sin()) on bar due to magnetic field

I = E /R

• Magnitude of current

Clockwise (+ charges go down thru bar, up thru bulb)

To left, slows down

Moving bar acts like battery E = vBL

B

-+

V

What changes if B points into page?

= vBL/R

Motional EMF, Preflight 14.1

F = q v B sin()

Which of the following statements is true? • positive charge accumulates at the top of the bar, negative at the bottom • since there is not a complete circuit, no charge accumulates at the bar's ends• negative charge accumulates at the top of the bar, positive at the bottom

L v

B

Motional EMF, Preflight 14.1

F = q v B sin()+ v

+-

-

+

|ΔV| |ΔU| = Fd

EMF = q v B sin() L/q

= v B L

B

L v

Velocity

Velocity

Moving + charge feels force downwards:

Moving + charge still feels force downwards: B

q q

Preflight 14.2

• Which bar has the larger motional emf? a b

v

v

E = v B L sin()

is angle between v and B

Case a:Case b: v perpendicular to B

Preflight 14.4, 14.5

Increase Stay the Same Decrease

Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.

To keep the bar moving at the same speed, the force supplied by the hand will have to:

True False

To keep the bar moving to the right, the hand will have to supply a force in the opposite direction:

Preflight 14.4

• Increase• Stay the Same• Decrease

Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.

To keep the bar moving at the same speed, the force supplied by the hand will have to:

F = ILB sin()

B and v still perpendicular (=90), so F=ILB just like before!

Preflight 14.5

• True• False

Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.

To keep the bar moving to the right, the hand will have to supply a force in the opposite direction.

Current flows in the opposite direction, so force from the B field remains the same!

Magnetic Flux

• Count number of field lines through loop.

Uniform magnetic field, B, passes through a plane surface of area A.AMagnetic flux = B A

Magnetic flux B A cos() is angle between normal and B

B

Anormal

B

Note: The flux can be negative(if field lines go thru loop in opposite direction)

Preflight 14.7

Compare the flux through loops a and b. 1) a>b 2) a< b

ab

nn B

A = B A cos(0) = BAB = B A cos(90) = 0

Lenz’s Law (EMF Direction)Emf opposes change in flux

• If flux increases: New EMF makes new field opposite to the original

field (to oppose the increase)• If flux decreases:

New EMF makes new field in the same direction as the original field (to oppose the decrease)

Preflight 14.9

The magnetic field strength through the loop is cut in half (decreasing the flux). If you wanted to create a second magnetic field to oppose the change in flux, what would be its direction?

a

nB

a

nB

LeftRight

The original flux is to the right and decreasing. To oppose the change and keep the total field strength the same, add another field in the same direction.

Which loop has the greatest induced EMF at the instant shown below?

1 2 3

33% 33%33%

1. Loop 12. Loop 23. Loop 3

W

vv

L 1

32

v

Which loop has the greatest induced EMF at the instant shown below?

1 2 3

33% 33%33%

1. Loop 12. Loop 23. Loop 3

W

vv

L 1

32

v

E 1 = vBL

E 3 = vBW

1 moves right - gets 4 more field lines.2 moves down - gets 0 more field lines.3 moves down - only gets 2 more lines.

E 2 = 0

1 is gaining flux fastest!

Change Area II

V

t=00=BLW

tt=BL(W+vt)

tBLWvtWBL

ttt

)(

00 vBL

L

W

V

W vt

EMF Direction: B is out of page and is increasing so EMF creates B field (inside loop) going into page.

I

EMF Magnitude:

= B A cos()

As current is increasing in the solenoid, what direction will current be induced in the ring?

1 2 3

33% 33%33%

1. Same as solenoid2. Opposite of solenoid3. No current

As current is increasing in the solenoid, what direction will current be induced in the ring?

1 2 3

33% 33%33%

1. Same as solenoid2. Opposite of solenoid3. No current

Solenoid current (counter-clockwise) B-field (upwards) => Flux thru loop • EMF will create opposite B-field (downwards)• Induced loop current must be clockwise

Which way is the magnet moving if it is inducing a current in the loop as shown?

1 2

50%50%

1. up2. down

S

N

NS

Which way is the magnet moving if it is inducing a current in the loop as shown?

1 2

50%50%

1. up2. down

S

N

NS

If the resistance in the wire is decreased, what will happen to the speed of the magnet’s descent?

1 2 3

33% 33%33%

S

N

NS

1. It will fall faster2. It will fall slower3. It will maintain

the same speed

If the resistance in the wire is decreased, what will happen to the speed of the magnet’s descent?

1 2 3

33% 33%33%

S

N

NS

1. It will fall faster2. It will fall slower3. It will maintain

the same speed

larger induced current, stronger magnetic field

Change A flat coil of wire has A=0.2 m2 and R=10. At time t=0, it is

oriented so the normal makes an angle 0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF.

n

B

A

if

if

ttt

i = B A cos(0)

f = B A cos(30)

= 6.43x10-3 VoltsWhat direction is the current induced?

5.0))0cos()30(cos( BA

upwards and decreasing. New field will be in same direction (opposes change). Current must be counter clockwise.

Magnetic Flux Examples

A conducting loop is inside a solenoid (B=onI). What happens to the flux through the loop when you…Increase area of solenoid?

Increase area of loop?

Increase current in solenoid?

Rotate loop slightly? B A cos()

Magnetic Flux Examples

A conducting loop is inside a solenoid (B=onI). What happens to the flux through the loop when you…Increase area of solenoid? No changeIncrease area of loop? IncreasesIncrease current in solenoid? IncreasesRotate loop slightly? Decreases

B A cos()

Magnetic Flux II

Increase area of solenoid Increases

Increase area of loop No change

Increase current in solenoid Increases

A solenoid (B=onI) is inside a conducting loop. What happens to the flux through the loop when you…

B A cos()