Physics 2212 K
Quiz #4
Solutions
Summer 2009
²
0
Permittivity constant
m
p
Mass of a proton
μ
0
Permeability constant
m
e
Mass of an electron
e
Fundamental charge
c
Speed of light
K
Coulomb constant
g
Acceleration due to gravity
Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal.
Any integrals in freeresponse problems must be evaluated.
I
. (24 points) An infinite slab of current has thickness
t
and uni
form area current density
J
out of the page.
What is the
magnitude of the magnetic field at a distance
d
above the
sheet?
Express your answer in terms of parameters defined
in the problem, and physical or mathematical constants.
.
.
.
.
.
.
.
.
.
.
.
.
.
Symmetry considerations show that the magnetic field points to the left above the slab, and to the right
below it. Use Ampere’s Law. Sketch a rectangular Amperian Loop of height 2
d
+
t
and width
s
. Then
I
~
B
·
~
ds
=
B
2
s
as
~
B
is parallel to
~
ds
at the top and bottom of the loop, and
~
B
is perpendicular to
~
ds
on the left and right
sides. The current passing through the loop can be found from the current density
I
through
=
Z
~
J
·
~
dA
=
JA
=
Jst
Putting these together in Ampere’s Law
I
~
B
·
~
ds
=
μ
0
I
through
⇒
B
2
s
=
μ
0
Jst
⇒
B
=
μ
0
Jt/
2
Quiz #4 Solutions Page 1 of 4
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1. (8 points) The switch in the illustrated circuit is set to position
“b” for a long time, then set to position “a” for a time
t
a
, then set
back to position “b”. After that, the current through the resistor
is
I
=
I
0
e

t
b
/RC
where
t
b
is the time from returning the switch to position “b”.
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 Summer '09
 Kindermann
 Charge, Acceleration, Gravity, Mass, Light, Magnetic Field, Electric charge, loop, eta /RC

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