Download Exam 2 Physics 195B (3/14/02)

Physics 196 Fall 2012
Exam 2
Time Allowed: Two hours
Some Physics Constants:
Name:
e = 1.6×10-19 C
k = 9.0×109 Nm2/C2
ε0 = 8.85×10-12 C2/Nm2
me = 9.11×10-31 kg
mp = 1.67×10-27 kg
electronic charge
Coulomb constant
Permittivity of free space
Mass of electron
Mass of proton
PART A (48 points total. 4 points each.)
1. The roof of a house measuring 4.0m ´ 5.0m is inclined at an angle of
30 with the horizontal. The electric field of the earth is
300 N / C downward. Find the electric flux through the roof when the
normal is chosen to point away from ground.
(a)
(b)
(c)
(d)
3, 000 N × m2 / C
-3, 000 N × m2 / C
5, 200 N × m2 / C
-5, 200 N × m2 / C
2. The diagram shows three point charges and two closed surfaces. The charge
on one is known to be q while the charges q A and qB on the other two are
unknown. The electric flux through the surface I is 4q e0 . The electric flux
through the surface II is -q e0 . Determine the charges q A and qB .
(a)
(b)
(c)
(d)
qA = 2q
qA = 3q
qA = 3q
qA = 4q
qB = -3q
qB = -2q
qB = -4q
qB = -5q
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3. In a region where there is an electric field, the work done by the electric force when an electron moves from
point A to point B is a positive quantity. Assuming electric force is the only force on the electron, which of
the following statement(s) is (are) correct?
(a)
(b)
(c)
(d)
The electric potential at A is higher than that at B.
The electric potential at B is higher than that at A.
The kinetic energy of the electron is higher at A than at B.
The kinetic energy of the electron is higher at B than at A
4. On the x-y plane, the electric field is uniform and is given by E = -500iˆ(N / C). The point A has
coordinates ( 2,-1) and the point B has coordinates (-1,3) where coordinates are measured in meters. The
potential difference VB -VA is
(a)
(b)
(c)
(d)
-1, 500 V
-1, 200V
+1, 200 V
+1, 500V
5. In a rectangular coordinate system (x, y, z) in space where coordinates are measured in meters, the electric
field is given by E = 6x 2iˆ ( N C ) . Find the electric potential difference V -V between the plane A at x =1
B
A
and the plane B at x = 3 .
(a)
(b)
(c)
(d)
-74 V
74 V
-52 V
52 V
6. Name two reasons why the following drawing of electric field lines and equipotential surfaces are incorrect.
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7. On the x-y plane, the electric potential in volt is given by the function V x, y   3x 2 y  2 y 3 of the
coordinates x, y in meters. Determine the components of the electric field in V/m at the point (-1, 2) are
(a) E x  12,
E y  15
(b) E x  12,
E y  21
(c) E x  12,E y  15
(d) E x  12,
E y  21
8. The linear charge density of a charged rod occupying the length between the points x = 0 and x = 3 on the xaxis is given the function l ( x ) = C x 2 + 3x where C is a constant. The electric potential it produces at the
(
)
point x = -3 is
(a) k C 2
(b) kC
(c) 3kC 2
(d) 9kC / 2
9. Two conducting spheres of radius 10cm and 30cm respectively are very far apart. Initially, the large sphere
carries a charge of 8.0mC while the small sphere is electrically neutral. They are then connected together by
a very long conducting wire. How much charge does the small sphere receive?
(a)
(b)
(c)
(d)
4.0mC
3.0mC
2.0mC
1.0mC
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10. The electric potential of an isolated metallic spherical shell of radius R is 40 kV when the potential is taken
to be zero at infinity. What is the electric potential produced by the charged shell at a point that is at a
distance 2R from the center?
(a) 10 kV
(b) 20 kV
(c) 80 kV
(d) cannot be determined
without knowing the value of R.
11. Circle the incorrect statement(s) when the electric potential in a capacitor is increased.
(a)
(b)
(c)
(d)
The energy will increase
The charge will increase
The capacitance will increase
The capacitance will decrease
12. Find the equivalent capacitance of the combination of capacitors as shown,
where the capacitances are all equal to C .
(a)
(b)
(c)
(d)
4C
3C
7C
3C
3
4
3
7
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PART B (52 points total)
13. (16 points) A parallel plate capacitors consists of two square plates of dimensions 60cm ´ 60cm separated
by a distance of 2.0cm . The plates are connected to a voltage source of 800 V .
(a) (4 points) Determine the capacitance
(b) (6 points) Determine the charge, the energy stored, and the electric field between the plates
(c) (6 points) With the power supply still connected to the capacitor, a piece of 2.0cm thick dielectric of
dimensions 20cm ´ 60cm and dielectric constant 3.0 is inserted between the plates. Find (1) the new
capacitance, (2) the work required to push the dielectric in place.
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14. (20 points) Two point charges lie on the x-axis on the x-y plane
as shown. They consist of a point charge -4.0nC at the point
(-1, 0) and a point charge 3.0nC at the point ( 2, 0) . All
coordinates are in meters.
(a) (4 points) Sketch below the electric potential function
V ( x, 0)
(b) (4 points) Determine the x-coordinates of two points where the potential vanishes.
(c) (4 points) Find the electric potential at the point P on the y-axis with coordinates (0, 3)
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(d) ( 4 points) Find how much work is required to bring a third point charge of -2.0nC from the point P to
the origin.
(e) (4 points) Find the electrostatic energy of the system of three point charges on the x-axis that results
after the step in (d).
15. (16 points) A solid sphere of radius a carrying total charge q
uniformly distributed throughout its volume is surrounded by a
concentric conducting spherical shell of inner radius 2a and outer
radius 2.5a . The shell carries total charge 2q
(a) (6 points) Denoting the distance of a point from the center by r ,
determine the electric fields at the following points (1) r = 3a ,
(2) r  2.25a , (3) r =1.5a (The answers should be in terms of
the Coulomb constant k , the charge q , and the length a )
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(b) (4 points) Determine the electric field at the point r = 3a 4
(c) (3 points) Determine the potential difference V ( r = a) -V ( r = 2a) between the points r = a and r = 2a .
(d) (3 points) Determine the electric potential of the shell, assuming the potential to be zero at infinity.
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