PHYS2424 – FALL 2000
EXAM #1 – Part 2
Electric Force, Fields, Potential, Capacitance, and Circuits
NAME: __________________________________________________________
Problem 1: __________________________________
(30 points)
Problem 2: __________________________________
(15 points)
Problem 3: __________________________________
(15 points)
Problem 4: __________________________________
(35 points)
Problem 5: __________________________________
(50 points)
Problem 6: __________________________________
(20 marks)
Problem 7: __________________________________
(20 marks)
Problem 8: __________________________________
(40 marks)
Problem 9: __________________________________
(30 marks)
Problem 10:__________________________________
(30 points)
Problem 11: __________________________________
(25 points)
Total Part 2 __________________________________
(310 marks)
1.
The electrostatic potential in a certain region of space is given by
3
2
2
V  3x z y  2xyz  3y volts, where x, y and z are in meters.
A.

Calculate the electric field E within this region in terms of x and y.
B.

Assuming that point (1.50m, 3.00m) is within this region of space, calculate E at
point (1.50m, 3.00m).
2.
In the figure below, all the resistors have the same resistance. If the ammeter
reads 2 A and the voltmeter reads 15 V, what is the resistance of each resistor?
R
R
A
R
V
V
3.
An ammeter A, which measures current, is connected between points a and b in
the circuit below. It is noted that the current through the ammeter is zero. Rx is a
resistor of unknown value, whereas R, 2R, and 3R are known. What is the value
of Rx?
a
3R
R
A
Rx
2R
b
4.
An overpaid assistant professor is performing an experiment in his penthouse
apartment. In this experiment, two identical charged balls of mass 10 kg and
unknown charge Q are suspended by thread from the ceiling as shown in the
figure. Assuming that the radius of the balls is negligible (treat as point charges),
4m
20 
20 
what is the charge Q on each of the balls?
4m
5.
Three isolated point charges q1, q2 and q3 are arranged as shown below:
y
q1 = 6.00 C
x
x
q1
q2 = 6.00 C
q2
q3 = - 3.00 C
x = 3.00 cm
y
y = 4.00 cm
q3
x
A.
Calculate the magnitude and direction of the electric field (due to q1, q2 and q3) at
the origin.
B.
Calculate the magnitude of the acceleration imparted to an electron placed at rest
at the origin.
C.
What is the electric potential at the origin? (Use r = , as your zero potential
reference point)
D.
What is the electrical potential energy stored in this charge configuration?
6.
What is the electric potential difference between point B and point A on the xaxis, if the x-component of the electric field varies along the x-axis as shown
below:
Ex (N/C)
A
6
3
-6
3
-3
6
9
x (m)
B
-3
7.
Calculate the total resistance for the circuit below:
R
7R
A
2R
3R
B
2R
8.
You are given the parallel plate capacitor shown below. Calculate the total
capacitance of this system assuming that the total plate area is 4.0 cm2.
o
3o
2o
4o
0.1 cm
0.1 cm
1.0 cm
1.0 cm
9.
Two charged metal plates in vacuum are 25cm apart as shown below. The electric
field between the plates is uniform and has a magnitude of 7.5 N/C. An electron
(mass = 9.1x10-31 kg) is released from rest just inside the negative plate.
E = 7.5 N/C
A.
+
+
-
+
-
+
-
+
-
How long will it take to reach the positive plate?
B.
How fast will the electron be going just before it hits the positive plate?
C.
If the positive plate of the capacitor has a net charge of 5.00 C, what is the
capacitance of the capacitor.
10.
For the circuit shown below:
20 v
6 k
20 k
30 k
15 k
10 v
5 k
4 k
Find the
A.
current through the 5 k resistor.
10B.
Find the voltage across the 20 k resistor.
10C.
Find the power dissipated by the 30 k resistor.
11.
The spherical device shown below consists of a uniformly charge solid sphere of
radius 1.0 cm, dielectric constant 2.0 with a total charge of +4 C. It is
surrounded by a hollow metal conductor of inner radius 4.0 cm and outer radius
of 6.0 cm containing a total charge of -2 C.
Using Gauss' Law of Electrostatics and any other physics necessary to sketch a
graph of the magnitude of the electric field versus radial distance for this device
making sure to indicate on your graph the location of each surface in the device
and the magnitude of the electric field at each surface.
E
r
Problem 11 (Continuation Page)