rod , find the velocity v(t) at arbitrary time.
Solution:
i Blv M N
Magnetic force (Ampere force):
F IBl B2l 2v R
N
R
l F
B
I
v
M
o
x
G L Pollack and D R Stump
7
Sec7-2 Motional and induced EMF
Fe eEk
Fm
Ek
Fe
Fm v
e
B
i
OP Ek dl
(v B) dl
OP
+B + +P+++ + + +
+ + Fe+ + + + +
v + + + - + + + +
+
+Fm+
-
+ -
+
+
+
+ + + O+ + + +
l
i
vBdl vBl
0
G L Pollack and D R Stump
G L Pollack and D R Stump
8
Sec7-2 Motional and induced EMF
Example 3 A long straight wire carrying a current I and a semicircle wire are coplanar. The semicircle wire moves at a velocity v parallel to the current of the straight wire. Find the induced emf in the semicircle wire.
The time dependence produces physical phenomena that are not present for static fields – electromagnetic induction and the displacement current.
G L Pollack and D R Stump
G L Pollack and D R Stump
3
Sec7-2 Motional and induced EMF
1. Motional EMF
The non-electrostatic force of the motional
EMF originates in Lorentz force.
Fm (e)v B
4
Sec7-2 Motional and induced EMF
i
b a
vB
dl
Steps solving the motional EMF：
a
（1）Choose dl
（2）Determine the direction of v B
by the right hand rule.
b
dl
G L Pollack and D R Stump

Sec7-2 Motional and induced EMF Example1 Find the emf of a rotating rod OP in B.
Solution:
di (v B) dl
vBdl
L
i
vBdl
0
L
0 lBdl
B
v
（3）Using i
b a
vB
dl
to calculate EMF.
i 0 EMF direction is the same as “ integral direction”.
i 0 EMF direction is opposite to “integral direction”.
Chapter7 Electromagnetic Induction
So far we have studied only fields that are independent of time.
Now we will be concerned with electric and magnetic fields, E(x,t) and B(x,t) , that vary with time.
2) A conductor does not move, and the magnetic
field changes with time, which leads to induced
EMF.
EMF
I
Ek
+-
Ek : non-electrostatic field
Ek dl
EMF of a closed circuit l Ek dl
1
Chapter 7 Electromagnetic Induction Contents
Sec7-1 Faraday’s law of electromagnetic induction Sec7-2 Motional and induced electromotive force Sec7-3 Self-inductance and mutual inductance Sec7-4 Energy of magnetic fields
F IBl B2l 2v R
Motion equation of the rod:
m dv B2l 2v
dt
R
v
dv
t B2l 2 dt
v v0
0 mR
v(t)
v e(B2l2 0
mR)t
N
Rl B F
v
M
o
x
R: resistance; m: mass of the rod; l: length of the rod
G L Pollack and D R Stump
2
Sec7-2 Motional and induced EMF
1) A conductor moves in magnetic field, and the area of a loop and the orientation change, which leads to motional EMF.
i
1 2
B L2
+ +
+ +
+ +
+ + + dl+
++ P
++
+ + v +B+
++
o
++
+ +
+ +
+ +
+++++++
i direction O
P
G L Pollack and D R Stump
6
Sec7-2 Motional and induced EMF
Example 2 Given initial velocity v0 of a metal