PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
SCORE BOX
Write your name on each page.
Page 1
(8)
Page 2
(12)
Page 3
(18)
Page 4
(15)
No books or notes are permitted in this examination. Writing
instruments and a calculator are the only items that you will need.
Page 5
(13)
A separate sheet of equations and constants is provided for your
convenience. These equations and constants are assumed known.
Any other equations or constants that you use must be derived from
these for full credit.
Page 6
(18)
Page 7
(16)
Total
(100)
Questions 1–8 will be graded on the basis of the answers to each
part only; no partial credit will be given for these questions.
For problems 9–12, unless explicitly stated otherwise, you must
show all your work. An answer will not be enough; understanding
must be demonstrated as well. This can take the form of a clear
calculation or, where appropriate, a clear written explanation. Partial credit will be awarded for taking the right steps to solve these,
even if you get the wrong answer.
1. In the vicinity of two point charges, one positive and one negative,
(a)
(b)
(c)
(d)
(e)
(f)
~ , must also be zero there.
if the electric potential, V, is zero at a point, the electric field, E
V is zero at some point along the line between the two charges.
~ is zero at all points, if the charges are equal in magnitude.
E
V is zero at all points, if the charges are equal in magnitude.
~ is zero at some point along the line between the two charges.
E
None of the above is true.
ANSWER[
]
(4 points)
2. A perfectly conducting metal sphere of radius R, which carries a net positive charge, +q, sits near a smaller
perfectly conducting metal sphere of radius R/3, which is neutrally charged. Then the two spheres are
connected together by a thin conducting wire. Afterwards,
(a)
(b)
(c)
(d)
(e)
Both spheres are at the same potential and both carry the same charge.
The charges on and the potentials of the spheres are the same as before the wire was connected.
Both spheres are at the same potential, but the larger carries the greater positive charge.
Both spheres are at the same potential, but the smaller carries the greater positive charge.
The larger sphere is at a higher potential than the smaller sphere and both spheres carry the same
charge.
ANSWER[
αβγδ
]
(4 points)
-1-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
3. When a negative charge is released and moves along an electric field line, it moves to a position of
(a)
(b)
(c)
(d)
(e)
lower potential and lower potential energy.
lower potential and higher potential energy.
decreasing magnitude of the electric field.
higher potential and higher potential energy.
higher potential and lower potential energy.
ANSWER[
]
(4 points)
4. The electric field lines in the figure to the left correspond to the field configuration of:
(a) Two equal positive charges;
(b) Two charges +Q and -Q;
(c) Two equal negative charges;
(d) Two unequal charges with negative the larger;
(e) Two unequal charges with positive the larger.
ANSWER[
]
(4 points)
5. An uncharged spherical conducting shell surrounds a charge −q at the center of the shell. Then charge
+3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and
outer surfaces of the shell are respectively
(a)
(b)
(c)
(d)
(e)
+2q , +q
+q , −q
−q , +q
+q , +2q
+3q , 0
ANSWER[
αβγδ
]
(4 points)
-2-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
6. A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them. When it
is connected to a battery of voltage ∆V0 , it has charge of magnitude Q0 on its plates. It is then disconnected
from the battery and the plates are pulled apart to a separation 2d without discharging them. After the
plates are 2d apart, the new capacitance and the potential difference between the plates are
(a) C0 , 2∆V0
(b) 2C0 , 2∆V0
(c) 21 C0 , 21 ∆V0
(d) 21 C0 , ∆V0
(e) 21 C0 , 2∆V0
ANSWER[
]
(4 points)
7. The electric potential inside a charged solid spherical conductor in equilibrium
(a)
(b)
(c)
(d)
is always zero.
is constant and equal to its value at the surface.
decreases from its value at the surface to a value of zero at the center.
increases from its value at the surface to a value at the center that is a multiple of the potential at the
surface.
(e) is equal to the charge passing through the surface per unit time divided by the resistance.
ANSWER[
]
(4 points)
8. In the following figure, the dashed line denotes a
Gaussian surface enclosing part of a distribution
of four positive charges.
(a) Which charges contribute to the electric field at P?
(5 points)
(b) Is the value of the flux through the surface, calculated using only the electric field due to q1 and q2,
greater than, equal to, or less than that obtained using the field due to all four charges? (5 points)
αβγδ
-3-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
9. Three charges are arranged at three corners of a square
of side a = 0.20 m, as shown. The value of q is 4.0 µC .
y
-2q
(a) Find the components of the electric field at the
center of the square.
(10 points)
a
Ex =
Ey =
x
+2q
+3q
(b) Find how much additional charge and of what sign must be placed at the empty corner so that the
electric field at the center of the square points in the +y direction, i.e. has no x-component. (It is not
necessary to show a calculation for this part.)
(5 points)
αβγδ
-4-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
y
10. Three charges are arranged at three corners of a square
of side a = 0.20 m, as shown. The value of q is 4.0 µC .
-2q
a
x
+2q
+3q
(a) Find how much work an external force must do to move the +2q from its current location at the
origin to the empty corner.
(8 points)
(b) Find how much additional charge and of what sign must be placed at the empty corner so that the
electrostatic potential at the center of the square is zero. (It is not necessary to show a calculation
for this part.)
(5 points)
αβγδ
-5-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
11. An long, non-conducting cylinder of radius R carries a uniform volume charge density of ρ0 (C/m3 ). ρ0
is a constant.
~ in terms of ρ0 , R and r (and the usual constants) inside
(a) Use Gauss’s law to find the magnitude of E
the cylinder, i.e., for any r < R.
(6 points)
~ in terms of ρ0 , R and r (and the usual constants) outside
(b) Use Gauss’s law to find the magnitude of E
the cylinder, i.e., for any r > R.
(6 points)
(c) Find the electrostatic potential at the surface of the cylinder, (r = R). Take V = 0 at r = 0, i.e. on
the axis of the cylinder.
(6 points)
αβγδ
-6-
page total:
PHYSICS 42
First Hour Exam
Electromagnetism & Modern Physics
September 25, 2006
Name:
Rec.
12. A 3.0 µF capacitor is charged to a potential difference of 12.0 volts and is then disconnected from the
battery. When a second capacitor that is initially uncharged is connected in parallel with the first capacitor,
the potential difference drops to 4.0 volts.
(a) What is the capacitance of the second capacitor?
(8 points)
(b) Calculate the electrostatic energy stored in the parallel combination. Is it greater than, less than, or
the same as the energy stored on the 3.0 µF capacitor before the second capacitor was connected to
it?
(8 points)
αβγδ
-7-
page total: