2010 Final

FINAL PHY 9C (Mar. 18, 2010)
Every problem is worth 10 points
1. (22.45) A small conducting spherical shell with inner radius a and outer radius b is
concentric with a larger conducting sphere with inner radius c and outer radius d (b<c).
The inner shell has a charge of +2q, the outer shell has a charge of +4q. Calculate and
graph the magnitude of the electric field in the regions: r<a, a<r<b, b<r<c, c<r<d, d<r.
2. (23.47) In a region of space the electric potential is V(x,y,z)=Axy-Bx2+Cy. Calculate
the components of the electric field vector E(x,y,z).
Determine the points where E(x,y,z)=0.
C1
3. (24.59) What is the equivalent capacitance of the
network between points a and b? C1=C5=8.4 F,
C2=C3=C4=4.2F.
C2
b
C5
4. (25.76) A rod of length L and cross section A has a
variable resistivity of (x)=a+bx2, (0<x<L). What is
the resistance of the rod?
5. (26.64) What is the equivalent resistance of the
shown circuit. R1=R3=R5=1, R2=R4=2.
C4
R2
R1
V
6. (27.72) In a rail gun a conducting bar of mass m and
length L slides over horizontal rails that are connected
to a voltage source. The voltage source maintains a
constant current I across the bar. There is a constant
magnetic field B perpendicular to the plane of the rails.
What should be the length D of the rails to accelerate
the bar from rest at x=0 to a speed of v at x=D?
I
7. (28.62) A pair of rigid metal rods of length L lie
horizontally on a table. Their ends are connected by
identical conducting springs of force constant k and
negligible unstretched length. If a current I is run
through this circuit, the springs stretch to a length x to
counterbalance the repulsion of the rods, as shown.
Calculate x.
x
8. (29.10) A square of side L is in a uniform magnetic
field B, which is perpendicular to the plane of the
square. The field abruptly ends at x=0. The square is
pulled out of the field with velocity v. Calculate and
graph the EMF, induced in the square, as a function of
the coordinate of the center of the square.
C3
a
R3
R4
R5
x xx x x xx x x x
v
x x x x x x x x x x
x x x x x x x x x x
X=0
X=D
I
I
x
x
x
x
x
x
x
x
L
xx
x x
x x
x x
x
x
x
x
v
X=0

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