PHY2049 Fall 2006
1
Prof. Yasu Takano
Prof. Paul Avery
Dec. 11, 2006
Exam 4 Solutions
(
First answer is correct
)
1. (
Exam 1
) Consider a cylinder of radius 6 m and height 15 m. At each point on the cylindrical
surface, an electric field of 10 V/m points out radially. There is no electric field on the top and
bottom surfaces of the cylinder. What is the charge enclosed by the cylinder in coulombs?
(1) 5.0
×
10
−
8
(2) 2.5
×
10
−
8
(3) 1.7
×
10
−
8
(4) 8.3
×
10
−
9
(5) 3.3
×
10
−
8
We use Gauss’ law, and note that only the E field perpendicular to the curved surface contrib-
utes. Using the area of a cylinder, Gauss’ law yields
(
)
enc
0
2
/
E
rh
q
π
ε
=
, where r is the cylinder
radius and h is its height. Solving for the enclosed charge yields
8
enc
5.0
10
q
−
=
×
C.
2. (
WebAssign 24.5
) Two large, parallel, conducting plates are 1.2 mm apart and have equal and
opposite charges on their facing surfaces. An electrostatic force of 4
×
10
−
13
N acts on an elec-
tron placed anywhere between the two plates. What is the potential difference in volts between
the plates?
(1) 3000
(2) 360
(3) 1.88
×
10
6
(4) 1880
(5) 2250
The force on an electron is F = eE. The potential difference between two plates is Ed. Thus the
potential difference can be written V = Fd/e = 3000 V.

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