# 31. Examples using Faraday`s Law. Induced emf and Electric Field

```LENZ’S LAW EXAMPLE: (from Prob. 24, page 812)
A conducting loop of mass M, resistance R, width

w, and length l is dropped into a field B pointing out
of the page. It reaches a terminal velocity before
the top edge enters the magnetic field. Calculate
the terminal velocity.
w
y
v
LENZ’S LAW EXAMPLE: (from Prob. 22, page 811)
A rectangular coil with N turns, resistance R, length l and width w moves at
constant speed v into, through, and then out of a region containing a field

B pointing into the page/screen. Find the magnitude and direction of the
magnetic force on the coil as it (a) enters the field, (b) moves entirely within the
field, and (c) leaves the field.
l
w
v
INDUCED emf AND ELECTRIC FIELD
 Look at a conducting loop of radius r in a region of

magnetic field B pointing into the page/screen
o The magnetic flux through the loop is
 B  BA  B r 2
o If B is changing, there is an emf around the
d
r
I
Bin
(increasing magnitude)
dB
2
B
r







dt
dt
E
E
 Picture shows direction of current for
increasing B
r
 The induced current implies a tangential electric

field E in the conductor
E
Bin
E
(increasing magnitude)
IMPORTANT INSIGHT:
 Changing magnetic flux ALWAYS induces an electric

field E EVEN IF NO CHARGES PRESENT

dB

Connects E to d t
 work to move charge q around a loop is
 
d B
W  q  E  d s  q  q
dt
around
E
E
r
E
Bin
E
(increasing magnitude)
loop
 
d B



E
d
s

 Implies: around
dt
loop
o integral is around closed path
o  B is the flux through the area enclosed by the path
 This is one of MAXWELL’S EQUATIONS

o E field in this equation NOT electrostatic – does not end on charges
```