CSULA
Spring 2008
FINAL EXAM
PHYSICS 213
Professor: Rafael Obregon
Name (Last, First): _________________________________________________
I) CONCEPTUAL QUESTIONS (5 points ea): Answer these using the correct formulas and few
complete and grammatically correct English sentences. Note that selecting the correct answer will
be worth 1 point and the correct explanation will be worth the rest of the points.
1) In class we show that the electric field (at any distance) due to an
infinite plane of positive charge with uniform surface charge density 
is equal to:  / 2 o  .
Let’s place two infinite planes parallel to each other. The plane on the
left has a uniform charge density  , and the one on the right has
uniform charge density –. What is the magnitude of the electric field
between and outside of the two planes?
Explain using direction of the electric field.
2) An electron (–e) moves in the plane of this paper toward the top of the page. A magnetic field (B)
is also in the plane of the page and directed toward the left. What is the direction of the magnetic
force (FB) on the electron? (a) Toward the bottom of the page. (b) Toward the top of the page.
(c) Toward the right edge of the page. (d) Toward the left edge of the page. (e) Upward out of the
page. (f). Downward into the page.
Hint: Show a diagram and then use the right-hand rule.
FE. Page 1 of 10
3) Consider the circuit in the figure and assume that battery has no
internal resistance. The switch is closed, what is the current in the
battery just after the switch is closed?
(a) 0. (b) /2R. (c) /R. (d) 2/R. (e) Infinite.
Explain your answer using some related formula
4) Consider the magnetic field due to the current I in the
length of wire shown in the figure. Rank the points
A, B, and C (from greater to smaller) in terms of
magnitude of the magnetic field that is due to the

current in just the length element ds shown in the
figure.
Explain your answer using some related formula
FE. Page 2 of 10
II) SOLVE
1) A. (5 pts) Consider a capacitor of capacitance C that is being discharged
through a resistor of resistance R. Find the time interval (t) –in function of the
time constant ( = RC) – required for the charge q(t) to fall one-half its initial
value Q?
B. (5 pts) An insulating solid sphere of radius a has a uniform
volume charge density  and carries a total positive charge
Q
(see the figure). Using Gauss’s Law, calculate the magnitude of the
electric field at a point r > a.
FE. Page 3 of 10
2) A rod of length l has a uniform positive charge per unit length  and a total charge Q.
A. (4 pts) Write an expression (in function of ke, , and x) for the magnitude of the electric field

( dE ) at point P due to the segment of the rod (dx) having a charge dq.
B. (6 pts) By integrating the previous expression, show that the total magnitude of the electric
field at P can be written as ke Q / a(l  a) . (recall that  = Q/l )
FE. Page 4 of 10
3) A proton with mass mp and charge +e is released from rest at point
A in a uniform electric field with magnitude E. The proton
undergoes a displacement d to point B in the direction of the
electric field as shown in the figure.
A. (4 pts) Using conservation of the mechanical energy
( K  U  0 ), write the appropriate reduction of the
previous equation for the isolated system of the charge and the
electric field (in function of mp, e, V and vB)
B. (6 pts) By an appropriated manipulation of the previous equation, write an expression for the
final speed vB (in function of mp, e, E and d).
FE. Page 5 of 10
4) The ammeter shown in the figure reads 2.00 A.
RECALL:
o
o
1st of all you must establish a current direction (I) through the ammeter.
Then: Use Kirchhoff’s Rules
A. (1 pts) Write and expression for the junction rule
I  0
B. (4 pts) Write an expression for the loop rule (2 loops)
V  0
C. (5 pts) Solve to find: I1, I2 and .
FE. Page 6 of 10
5) A wire bent into a semicircle of radius R forms a closed circuit
and carries a current I. The wire lies in the xy-plane, and a

uniform magnetic field B is directed along the positive y-axis as
in the figure.
A. (5 pts) Determine the magnitude and direction of the
magnetic force (FB1) on the straight portion (in terms of I, R
and B).
B. (5 pts) For the curved section: first, write and expression for the infinitesimal magnetic force

dFB2 on the element ds , then integrate it to find the magnitude and direction of the force on
the curved part (in terms of I, R and B). (recall: ds = Rd).
FE. Page 7 of 10
6) A wire having a mass per unit length  = m/L carries a current I horizontally to the south. The

wire is in the presence of a magnetic field B (eastward orientated) enough to lift the wire
vertically upward (reaching equilibrium).
A. (4 pts) Using 2nd Newton’s Law write down an expression when the wire reaches the
equilibrium position (a body diagram will be helpful).

B. (6 pts) Using part A find an expression for the magnitude of the magnetic field B (in terms of
, g and I).
FE. Page 8 of 10
7) A current-carrying wire consists of two straight portions and a
circular arc of radius a, which subtends and angle  as shown in the
figure.
Hint: calculate first ds  rˆ  ds r sin  for each portion.
A. (4 pts) calculate the magnitude of the magnetic field at O due to
the straight segments AA’ and CC’.
B. (6 pts) calculate the direction and magnitude of the magnetic field at O due to the
curve segment AC (in terms of , a, I and constants). (recall Arc AC  s  R )
FE. Page 9 of 10
8) A cube of side 2.5 cm is positioned as shown in the figure. A

uniform magnetic field given by B  (5iˆ  4 ˆj  3kˆ)T exists
throughout the region. Using Gauss’s Law in Magnetism:
A. (6 pts) calculate the magnetic flux B through the shaded side.

Hint: find first a vector A in m2.
B. (4 pts) what is the total magnetic flux through the six faces?
FE. Page 10 of 10