Motional EMF - University Of IllinoisPhysics 212 Lecture 3 Music Who is the Artist? A) Gram Parsons B) Tom Waits C) Elvis Costello D) Townes Van Zandt E) John Prine Why? Theme of the

Physics 212 Lecture 16, Slide 1

Physics 212 Lecture 16

Motional EMF

Induced emf !! Conductors moving in B field

Physics 212 Lecture 3

Music Who is the Artist? A) Gram Parsons B) Tom Waits C) Elvis Costello D) Townes Van Zandt E) John Prine

Why?

Theme of the week? Guys who sing with Emmylou Harris !! I do like these albums.. Giving you a break from Jazz this week…


f dl

Closed loop integral, so …

Ff

q

Electromotive Force (EMF): Force per

unit charge of ANY sort

e.g.:

Bf v B

Ef E

where

To get a non-zero EMF, need a force that can

push charges around a loop, i.e.

Units of EMF: work = force x distance EMF = force/q x distance = work/q =


The Big Idea When a conductor moves through a region containg a magnetic field:

Magnetic forces may be exerted on the charge carriers in the conductor: Creates an -> potential difference across the ends of the bar:

05

v

X X X X X X X X X B

X X X X X X X X X

+ - F

F

BF qv B

L

due to ( )B BV f dl v L vBLB This is called MOTIONAL EMF:

Move a conductor in a magnetic field in the right way, and you’ve got a magnetic battery

in above example


Putting it together

Change Area of loop Change magnetic field

through loop Change orientation of loop relative to B

Faraday’s Law

B A d

dt

We will study this law in detail & in another context next time !


Rotate picture by 90o (top view)

v

X X X X X X X X X

B

X X X X X X X X X

X v

b a

:22

Bar a No magnetic force

on charges No charge separation

No emf

Checkpoint 1

A B C D

+ -

v || B Fa = 0

+ - F

F

Fb = qvB

Bar b Magnetic force on charges

Charge separation emf = (F/q)L = vBL

Two identical conducting bars (shown in end view) are moving through a vertical magnetic

field. Bar (a) is moving vertically and bar (b) is moving horizontally.

Which of the following is true?

A. A motional emf exists in the bar for case (a), but not (b)

B. A motional emf exists in the bar for case (b), but not (a)

C. A motional emf exists in the bar for both cases (a) and (b)

D. A motional emf exists in the bar for neither case (a) nor case (b)

B

Physics 212 Lecture 16, Slide 11 :22

Rotate picture by 90o

A B C D

Checkpoint 2a

A B

Changing Area

A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.

The entire apparatus is placed in a uniform magnetic field pointing

into the screen, and the bar is given an initial velocity to the right.

The motion of the green bar creates a current through the bar

A. going up

B. going down


Rotate picture by 90o

A B C D

v0

X X X X X X X X X

B

X X X X X X X X X

+ - F

F

Fb = qv0B

Bar Opposite forces on charges

Charge separation emf = (F/q)L = v0BL

Checkpoint 2a

A B

V R

I

Equivalent circuit

Changing Area




The motion of the green bar creates a current through the bar

A. going up

B. going down


A B C D

Preflight 5

Counterclockwise Current

I

BLIF

Energy External agent must exert force F to the right to maintain constant v0 This energy is dissipated in the resistor!

LBR

vBLF

RILBv

R

vBLFvP 2

Checkpoint 2b

Changing Area

F points to left

F

A B C D E




The current through this bar results in a force on the bar

A. down

B. up

C. right

D. left

E. into the screen

Physics 212 Lecture 16, Slide 14 20

Checkpoint 5

A wire loop travels to the right at a constant velocity. Which plot best represents the induced

current in the loop as it travels from left of the region of magnetic field, through the magnetic

field, and then entirely out on the right side?

B = 5 T

Out of Screen

B = 0

v


Checkpoint 5

Let’s step through this one




B = 5 T

Out of Screen

B = 0

v


v

Only leading side has charge separation emf = BLv (cw current)

L +

- fB

v +

- fB L

+

- fB

Leading and trailing sides have charge separation emf = BLv – BLv = 0 (no current)

Only trailing side has charge separation emf = BLv (ccw current)

t

t

t v L

+

- fB

A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in

the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely

out on the right side?








Checkpoint 5




B = 5 T

Out of Screen

B = 0

v


Changing B field A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying

current as shown.

What is the direction of the induced current in the loop?

A. clockwise

B. counter-clockwise

C. there is no induced current in the loop

Checkpoint 3


I

B B

B B

v + -

+ -

Changing B field A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying

current as shown.

What is the direction of the induced current in the loop?

A. clockwise

B. counter-clockwise

C. there is no induced current in the loop

Checkpoint 3


Generator: Changing Orientation

22

On which legs of the loop is charge separated?

A) Top and Bottom legs only B) Front and Back legs only C) All legs D) None of the legs

Bv

parallel to top and bottom legs

Perpendicular to front and back legs



22

At what angle q is emf the largest?

(A) q = 0 (B) q = 45o

(C) q = 90o

(D) emf is same at all angles

Bv

Largest for q = 0 (v perp to B)

L

w

)cos(cos)2

(2222 tABBw

LBvLLq

FEL q

= v


Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown.

The side view of the loop is shown at a particular time during the rotation. At this time, what

is the direction of the induced (positive) current in segment ab?

A. from b to a

B. from a to b

C. there is no induced current in the loop at this time

Checkpoint 4



B

v

v X

Bv

Bv

I + -

A rectangular loop rotates in a region containing a constant magnetic field as shown.

The side view of the loop is shown at a particular time during the rotation. At this time, what

is the direction of the induced (positive) current in segment ab?

A. from b to a

B. from a to b

C. there is no induced current in the loop at this time

Checkpoint 4


Example Problem

I v

x L

h

A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?

•Conceptual Analysis:

•Long straight current creates magnetic field in region of the loop.

•Vertical sides develop emf due to motion through B field

•Net emf produces current

•Strategic Analysis:

•Calculate B field due to wire.

•Calculate motional emf for each segment

•Use net emf and Ohm’s law to get current


Example Problem

I v

x L

h


What is the direction of the B field produced by the wire in the region of the loop?

A) Into the page

B) Out of the page

C) Left

D) Right

E) Up


Example Problem

I v

x L

h


What is the emf induced on the left segment?

A) Top is positive

B) Top is negative

C) Zero

B into page

Bv


Example Problem

I v

x L

h


What is the emf induced on the top segment?

A) left is positive

B) left is negative

C) Zero

B into page

Bv

perpendicular to wire


Example Problem

I v

x L

h


What is the emf induced on the right segment?

A) top is positive

B) top is negative

C) Zero

B into page

Bv


Example Problem

I v

x L

h


Which expression represents the emf induced in the left wire

B into page

(A)

(B)

(C)

Lvx

Ioleft

2

vBE qEqvB vBhEh

hvx

Ioleft

2

LvxL

Ioleft

)(2

x

IB o

2 hv

x

Io

2


hvxL

Ioright

)(2

Example Problem

I v

x L

h


Which expression represents the emf induced in the right wire

B into page

(A)

(B)

(C)

hvx

Ioright

2

Lvxh

Ioright

)(2

vBE qEqvB vBhEh

hvxL

Io

)(2

)(2 xL

IB o


hvxL

Ihv

x

I ooloop

)(22

Example Problem

I v

x L

h


Which expression represents the total emf in the loop?

B into page

(A)

(B)

(C)

hvxL

Ihv

x

I ooloop

)(22

0loop

RI

looploop

xLxhv

R

II oloop

11

2


Follow-Up

I v

x L

h

A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps.

What is the direction of the induced current?

B into page

(A)

(B)

Clockwise

Counterclockwise

+ +

- -

Left > Right

I

Clockwise current


Follow-Up

I v

x L

h

A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps.

What is the direction of the force exerted by the magnetic field on the loop?

B into page

(A)

(B)

UP

DOWN

I

(C) LEFT

(B) RIGHT

(B) F = 0

I

B into page

Total force from B Points to the left !!

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Motional EMF - University Of IllinoisPhysics 212 Lecture 3 Music Who is the Artist? A) Gram Parsons B) Tom Waits C) Elvis Costello D) Townes Van Zandt E) John Prine Why? Theme of the