1) An insulating sphere with radius R has a uniform positive volume charge
density of ρ. A solid metallic shell with inner radius R and outer radius 2R has zero
total charge. [Express your answers for parts (a-d) using ρ, R, and constants]
(a) (2 pts) What is the magnitude of the electric field at a distance ? 3? away
from the center?
(b) (3 pts) Assuming the potential at infinity is 0. What is the potential at the outer
surface (? 2?) of the metallic shell?
(c) (3 pts) What is the potential at the inner surface (? ? of the metallic shell?
(d) (6 pts) What is the potential at the center of the insulating sphere (? 0)?
(e) (4 pts) If the metallic shell is replaced with an insulating shell with inner radius R
and outer radius 2R that has no charge anywhere. The insulating core remains the
same. Circle below which one(s) of the previous questions will have a different
answer? XXXXXXXXXXa. b. c. d.
2R
R
insulator
conductor
2R
R
insulator
insulator
(f) (6 pts) Two long straight parallel conductors are a distance 4? apart center-to-center. A thin-walled cylindrical shell
with its center at ? 0 has radius ? and ca
ies a cu
ent 3? along the ? direction. A wire at ? 4? ca
ies a cu
ent
? also along the ? direction.
What is the magnitude of the magnetic field at ? 2?? [Express your answers using ?, ?, and constants]
(g) (6 pts) Find the coordinate of the location on the ?-axis where the total magnetic field is 0. [Express your answers
using ?, ?, and constants]
2) An infinite long wire ca
ies a cu
ent ? ? ? cos ?? . Nea
y, there is a
triangular loop at a distance ? from the long wire, with base ? and height ?. The
loop has electrical resistance R. [Express answers in terms of ?, ?, ?, ?, ?0, ? and
as appropriate]
(a) (5 pts) At which instants in time is there zero induced cu
ent in the loop,
during the range 0 ? 2?/??
(b) (5 pts) When is the induced cu
ent flowing clockwise as viewed in the figure,
during the range 0 ? 2?/??
(c) (11 pts) What is the magnitude of the induced cu
ent in the loop? Express your answer as a function of time t.
(d) (3 pts each part) For your convenience, the same exact figure on the previous page is repeated here
What is the direction of the force on the loop when:
(i ? 0? Circle one: (no force, attracted to wire, repelled by wire)
(ii) ? ?/ 4? ? Circle one: (no force, attracted to wire, repelled by wire)
(iii) ? ?/ 2? ? Circle one: (no force, attracted to wire, repelled by wire)
3) Consider the circuit shown below, where the EMF of the battery is ? 5.00 V, ?1 ?2 10.0 Ω and ?3 5.00 Ω,
? 10.0 μH and ? 40.0 μF. The capacitor starts out uncharged and the inductor is not energized in any way.
Assume that all wires shown
connecting these components are
perfect ideal conductors. You must
show all your work!
(a) (6 pts) At time ? 0, the switch S1
is closed while switch S2 remains open.
Immediately after this, what is the
potential difference across resistor ?1?
(b) (6 pts) After a very long time with switch S1 closed and switch S2 open, what is the cu
ent through ?3?
(c) (4 pts) After a very long time with S1 closed and S2 open, the switch S1 is opened and simultaneously switch S2 is
closed. Immediately after this, what is the potential difference ? ? as labelled in the figure?
(d) (6 pts) How many seconds after S2 is closed will the magnitude of the charge on the capaciator first be at its
maximum?
(e) (8 pts) What is the maximum magnitude of the charge on the capaciator? When it first reaches that maximum, what
will be the potential difference ? ? ?
4) A radio tower near Philadelphia
oadcasts at a frequency of 88.5 MHz (WXPN) and emits 50,000 W uniformly in a
hemisphere above the ground. You want to detect the radio wave n Penn cam a distance of 12,000 m away from
the tower, with a circular wire loop with radius 5.00 cm.
(a) (3 points) What is the wavelength of the radio wave?
(b) (3 points) What is the intensity of the radio wave on campus?
(c) (3 points) If the wave reflects off a metal plate with area 0.400 m2 on campus, then what is the force on the plate?
Assume the plane of the metal plate is perpendicular to the wave s direction of travel.
(d) (3 points) If the radio wave passes through a window with area 0.400 m2 on campus, then how much energy passes
through the window in 30.0 seconds? Assume the plane of the window is perpendicular to the wave s direction of travel.
(e) (6 points) What are the maximum values of the electric and magnetic fields on campus?
(f) (3 points) If the x-axis points from the tower to campus, and the electric field is polarized along the y-axis, then what
is the optimal orientation of the circular loop on campus? Circle one of the following for the orientation of the plane of
the circular loop: x-y plane, XXXXXXXXXXx-z plane, XXXXXXXXXXyz- plane.
(g) (9 points) What is the maximum induced EMF around the circular loop on campus?