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Material Type: Exam; Professor: Cattell; Class: Elec Magnetism & Light; Subject: Physics; University: Community College of Philadelphia; Term: Fall 2018;
Typology: Exams
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(See Figure 1.)
a.
2 2
2 2
1 (^1 ) 0 1
6 (^9) N m 5 N C^2 1 C
2 (^2 ) 0 2
6 (^9) N m 5 N
C^2 2 C
0.500 m
0.500 m
q E r E q E r E
Rx 2
5
(^4) N C
0 cos 210
Ry 1 2
5 5
(^4) N C
sin 210
(^4 4) N C
E 9.35 10 ˆ i^ 5.40 10 ˆ j (20 points)
b.
(^6 4 4) N C
2 2
2 2 2 2
2
2.16 10 N or 21.6 mN
F qE
i j
i j
2
2
F
arctan 1.87 10
30.0 below the + x axis or 330
c.
(^4 4) N C
4 4
4 4
: 1.50 3.00 C m 9.35 10 5.40 10
1.50 3.00 0 m N; 1.50 5.40 10 3.00 9.35 10 m N
0.200 m N (20 points)
p E
i j i j
i j k
k
k
Continued on the other side
(20 points)
0.500 m
x
y
Figure 1
q 1
E q 2
30
30
Figure 2
x
y
q 1
q 2
q
x
x
y
x 1 - x
x x 1
Charge q = x
lies in this interval.
Uniform charge
per unit length .
Figure 4
Flux through S:
S 1 2 3
d d d d
From symmetry E is directed radially away from the line of charge and has a constant magnitude over the
lateral side of S (side 3).
Over the sides 1 and 2 of S E and d A are perpendicular:
1 2
d 0; d 0
Over side 3 of S E and d A are parallel and E has constant magnitude E :
3 3
3 S
A 2 Thus 0 0 2
d Ed
E d E rL d E rL
Gauss' Law:
S^0 0
so 2 = and. 2
q L d q L E rL E r
E A (20 points)
2 1 0
0
(^2) L 2 (^0 1 )
0
0 1 0 1 1 L
1 1
0 1 1
0 1 1
Continued on the next page
(12 points)
2 1
1
1 2 2 2 2 1
2
1 1
: For let then and
(We may leave out the " " (why?))
dx Note u x x du dx
x x
dx du du u u du
x x u^ u^ u
dx C
x x x^ x
Infinite line of charge
with uniform linear
charge density .
Gaussian surface S in the form of a
right circular cylinder of radius r and
length L coaxial with the line of charge.
r
E From symmetry the electric field is directed radially away from
the line of charge.
2 1 3
d A
d A d A
Figure 3