Platt, David – Homework 21 – Due: Oct 28 2005, 4:00 am – Inst: Ken Shih
1
This
printout
should
have
8
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 2) 10 points
Given:
B
=
b t
, where
b
= 0
.
9 T
/
s (lower
figure).
Consider a changing magnetic field (from
B
0
to
B
, upper figure) within a circle of radius
4 m.
The magnetic field is pointing into the page
⊗
and its magnitude is increasing.
4 m
B
0
B
0
B
0
4 m
B
B
B
⇒
~
t
~
B
0
B
0
B
Find the direction of the induced emf
E
ind
.
1.
clockwise
2.
counterclockwise
correct
3.
out of the page
4.
into the page
Explanation:
Let :
a
= 4 m
and
b
= 0
.
9 T
/
s
.
Faraday’s Law of Induction:
E
ind
=
I
~
E
ind
·
d~s
=

d
Φ
B
dt
Lenz’s Law – Induced emf’s always oppose
magnetic flux changes.
Use a “bracket”, “[ ]”, to denote the direc
tions. The direction content of Faraday’s Law
then reads,
[
E
ind
] =

•
d
Φ
dt
‚
=
⊗
=
fl
.
The right hand rule then implies that the
direction of
E
ind
is counterclockwise.
This
is consistent with Lenz’s Law: the magnetic
field is increasing into the page, so the induced
emf
E
ind
creates a magnetic field out of the
page to counter this change.
002
(part 2 of 2) 10 points
Find the magnitude of the induced electric
field
E
ind
on the perimeter of the circular
magnetic field.
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 Fall '08
 Turner
 Physics, Work, Magnetic Field, Faraday, FC, Platt, Eind

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