PHYS2424 – SPRING 2001
EXAM #1 – Part 2 (Version A)
Electric Force, Fields, Potential, Capacitance, and Circuits
NAME: __________________________________________________________
Problem 1: __________________________________
(35 marks)
Problem 2: __________________________________
(25 marks)
Problem 3: __________________________________
(15 marks)
Problem 4: __________________________________
(45 marks)
Problem 5: __________________________________
(15 marks)
Problem 6: __________________________________
(25 marks)
Problem 7: __________________________________
(35 marks)
Problem 8: __________________________________
(30 marks)
Problem 9: __________________________________
(40 marks)
Problem 10:__________________________________
(15 marks)
Total Part 2 __________________________________
(280 marks)
1.
A parallel-plate capacitor is constructed using three dielectric materials as shown
below.
L
L/2
K1
K2
d
K3
A.
d/2
Find an expression for the capacitance of the device in terms of the plate area A
and d, K1, K2, and K3.
B.
Assuming the values A = 1.0 cm2, d = 2.00 mm, K1 = 4.9, K2 = 5.6, and K3 =
2.1, calculate the energy stored in the device when the voltage across the
capacitor is 100 v.
2.
The electrostatic potential in a certain region of space is given by
V
4
2
 2x y  3x
3
volts, where x and y are in meters.
x2y
A.

Calculate the electric field E within this region in terms of x and y.
B.

Assuming that point (-1.00m, 2.00m) is within this region of space, calculate E at
point (-1.00m, 2.00m).
3.
Find the equivalent resistance between points a and b in the combination of
resistors shown below:
5
7
b
a
3
15
4.
Four point charges are at the corners of a square of side a as shown below.
2q
a
q
y
a
3q
A.
4q
Determine the magnitude and direction of the electric field at the location of
charge q.
x
B.
What is the resultant force on q?
C.
What is the electric potential at the center of the square due to these charges? (Use
r = , as your zero potential reference point)
D.
What is the electrical potential energy stored in this charge configuration?
5.
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
18
2
9
-6
3
-3
6
9
x (m)
B
-9
6.
A rod of length L as shown below lies along the x-axis with its left end at the
origin and has a nonuniform charge density  = x (where  is a positive
constant).
y (m)
B
b
x (m)
L
A.
What are the units of ?
B.
Calculate the electric potential at point B that lies along the perpendicular bisector
of the rod a distance b above the x-axis.
6. Continued
7.
Consider the circuit shown below.
a
3.0 
5.0 
3.0 
10 
10 
4.0 
28 V
4.0 
A.
b
2.0 
3.0 
Calculate the current dissipated by the circuit in the 5.0- resistor.
B.
What is the power dissipated by the circuit? (Hint: What supplies the power?)
C.
Determine the potential difference between points a and b (i.e. Va-Vb)?
8.
In the circuit below, suppose that the switch has been closed sufficiently long for
the capacitor to become fully charged.
12 k
10 f
9.0 V
15 k
3.0 k
A.
Find the steady-state current through each resistor for the closed switch condition.
B.
What is the charge on the capacitor when it is fully charged?
C.
The switch is now opened at t = 0. Find the time that it takes for the current to fall
to one fifth of its initial value.
9.
For the configuration shown below, suppose that a = 5.0 cm, b = 20 cm, and c =
25 cm. Furthermore, suppose that the electric field at a point 10 cm from the
center is measured to be 3.6 x 103 N/C radially inward while the electric field at a
point 50 cm from the center is 2.0 x102 N/C radially outward.
c
Insulating
Sphere
b
a
A.
What is the net charge of the insulating sphere?
B.
What is the net charge on the conducting spherical shell?
Conducting
Spherical Shell
C.
What is the charge on the inner surface of the conducting spherical shell?
D.
What is the charge on the outer surface of the conducting spherical shell?
E.
Assuming that the insulating sphere is uniformly charged, make a sketch of the
radial electric field.
Er
r
10.
Electron beam accelerators are used to manufacture gem stones and certain
plastics by creating defects in the materials. In a certain accelerator, electrons
emerge with energies of 40.0 MeV (1 MeV = 1.6 x 10-13 J). The electrons do not
emerge in a steady stream, but in pulses that repeat 250 times per second. Each
pulse lasts for only 200 ns with the electrons in the pulse constituting a current of
150 mA as shown below.
200
ns
150
mA
Diagram of Three Electron Pulses
A.
How many electrons are delivered in each pulse?
B.
What is the average current delivered by the accelerator?
C.
What is the maximum power delivered by the electron beam?