Exam I Solutions
PHY2049
Summer 2011
(Ch. 21.53)
1.
Two small, positively charged spheres have a combined charge of 50 μC.
If each sphere is
repelled from the other by an electrostatic force of 1N when the spheres are 2.0 m apart, what is
the charge (in μC ) on the sphere with the smallest charge?
(A) 11.6
Suppose that the charges on the two spheres are q
1
and q
2.
Then q
1
+q
2
= 5x10
5
and F = k q
1
q
2
/r
2
means that q
1
q
2
= 4.44 x 10
10
.
At this stage, note that if we define q
1
and q
2
as respectively x and y μC,
then
we have x+y = 50 and xy =
4000/9 = 444.44.
There are several ways to solve these equations,
most direct being the substitution.
The answers for (x,y) are 11.6 μC and 38.4 μC.
(Ch. 22.5)
2.
What is the magnitude (in pC) of a point charge whose electric field 50 cm away has a
magnitude of 2V/m?
(A)
55.6
`
E = kq/r
2
which means that q = Er
2
/k = 5.56 x 10
11
C
(Ch. 23.7)
3.
A proton is a distance d/2 directly above the center of a sqaure of side d.
What is the magnitude
of the electric flux (in nN.m
2
/C) through the square?
(A) 3
It would be a sixth of the total flus through a cube which encloses the proton.
The answer is q/6ε
o
=
3.01x10
9
Nm
2
/C.
(Ch. 24.24)
4.
what is the net electric potential (in mV) at the origin due to the circular arc of charge
Q
1
=
+7.21 pC and the two particles of charges
Q
2
= 4.00
Q
1
and
Q
3
= 2.00
Q
1
? The arc's center of
curvature is at the origin and its radius is
R
= 2.00 m; the angle indicated is
θ
= 20.0°.
The
potential is taken to be zero at infinity.
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The potential is
(Ch. 25.68)
5.
The capacitances of the four capacitors shown in Fig.
2552
are given in terms of a certain
quantity
C
.
In ratio to C,
what is the equivalent capacitance between points
A
and
B
? (
Hint:
First imagine that a battery is connected between those two points; then reduce the circuit to an
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 Spring '08
 Any
 Physics, Charge, Force, Electric charge, power supply, 3 m, Kirchhoff, 2.0 m, nN.m2/C

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