Physics 202 MWF 10:20 Spring 1998 (Ford)
Exam I Chapts. 24-27 in SZY College Physics 7e
Show all your work. Partial credit will be given if earned. Write your
answers in the blanks provided.
(14 pts) 1. A small object with charge q = -4.00 × 10-3 C moves in a
region of varying electric potential. No forces are exerted on the
object except for the electric force associated with the electric potential.
At point A the electric potential is V = 8000 V and at point B the electric
potential is is V = 3000 V. At point A the object has
kientic energy 90 J. What is the kinetic energy of the charge when it is
at point B?
Ans. ____70 J____
(24 pts) 2. Point charges q1 = +2.0 × 10-9 C and q2 = -5.0 × 10-9 C are placed as shown in the sketch.
a) What are the x- and y-components of the resultant electric field at
the origin produced by this pair of point charges? (Be sure to say whether each
component is positive or negative.)
Ans. Ex = ____+2.23 N/C____
Ey = ____-0.432 N/C_____
b) What is the electric potential V at the origin produced by this pair
of point charges? (Be sure to say whether the potential is positive or
negative. Take the potential to be zero at large distances from the charges.)
Ans. ____-7.6 V_____
(22 pts) 3. A small sphere with mass 8.00 g hangs by a thread between two very
large parallel vertical plates 5.00 cm apart. The charge on the sphere is
q = -6.00 × 10-6 C.
a) What potential difference between the plates will cause the thread
to assume an angle of 37° with the vertical?
Ans. ___492 V____
b) Which plate in the sketch, a or b, is at higher potential?
Ans. ___b____
(18 pts) 4. A hollow conducting sphere has inner radius a and outer
radius b. The hollow sphere has a net charge -3q. A point charge +q
is placed in the hollow space at the center of the sphere, as shown in the
sketch. For each of the following questions to receive any credit you
must show clearly how you obtain your answer.
a) In terms of q and the distance r from the center of the sphere,
derive the expression for the magnitude of the electric field for
0<r<a (inside the hollow space).
Ans. ____q/4
0r
2 _____
b) In terms of q and the distance r from the center of the sphere,
derive the expression for the magnitude of the electric field for
r>b (outside the sphere).
Ans. ___2q/40r
2____________
c) In terms of q how much charge is on the inner surface of the sphere?
Ans. ___-q____
(22 pts) 5.
a) A capacitor with C1 = 4.0 µF and a capacitor with C2 = 6.0 µF
are connected in parallel across a 600-V source of potential difference.
Find the charge on each capacitor and the voltage across each.
Q1 ___2.4 × 10-3 C____
V1 ____600 V_____
Q2 ___3.6 × 10-3 C____
V2 ____600 V____
b) The charged capacitors are disconnected from the potential source and from
each other without the charge on them changing. They are then reconnected to
each other, with the positively charged plate of one connected to the negatively
charged plate of the other. After the charge has redistributed between the two
capacitors, what is the final charge on each capacitor and what is the
voltage across each capacitor?
Q1 ____4.8 × 10-4 C____
V1 ___120 V____
Q2 ____7.2 × 10-4 C____
V2 ____120 V____