Physics II
FALL2015
Homework #4 (Ch. 28-30)
Due: Oct.26, 2015
1. (10 pt) A metal disk with a radius 15 cm rotates with a frequency of 60
rev/s. A magnetic field of 6 T is perpendicular to the disk. A resistor of 45 
is connected between the center and the edge of the disk.
How much current will run through the resistor?
2. (10 pt) A proton with speed 3x107 m/s enters a region of
uniform magnetic field B=10 T, which is into the page, as
shown in the figure. The proton enters the magnetic field at
an angle 40 with respect to the normal of the field’s
boundary and the proton exits the magnetic field at an angle
 with respect to the normal of the field’s boundary at a
distance d from the place where the charged particle entered
the magnetic field. Find the angle  and d.
3. (10pt) A metal strip 2 cm wide and 0.1 cm thick carries a
current of 20 A in a uniform magnetic field of 2 T. The Hall
voltage is measured to be 4.27 V.
(a) Calculate the drift velocity of the electrons in the strip.
(b) Find the number density of the charge carriers in the strip.
(c) Which is at the higher potential, a or b?
4. (10 pt) When a conducting rod with its length l rotates with a
constant angular velocity  on a pivot point O and in a plane
perpendicular to a magnetic field B, find the induced emf between the
ends of this rod.
5. (10 pt) As shown in the figure, let’s consider a coil of N2 turns wound
around part of a toroid of N1 turns. The toroid’s inner radius is a, its outer
radius b, and its height h.
(a) Find the magnetic field inside the toroid as a function of a distance r (for
r<a, r>b and a<r<b) from the center of the toroid.
(b) Find the self-inductance L of the toroid.
(c) Find the mutual inductance M for the toroid-coil combination.
B
6. (10 pt) An electron rotates in a circular orbit (radius a) with an angular
velocity 
(a) Find the magnetic dipole moment  due to this electron’s circular motion.
(b) Find the magnetic field at the point P located on the central axis of the
circular orbit and separated by a distance x from the center of the orbit.
(c) When x>>a, show the magnetic field is proportional to 1/x3
7. (10 pt) In the circuit shown, the switch was connected to a
for a long time.
(a) When the switch connected to b, what is the frequency of
an oscillation in the LC circuit.
(b) What is the maximum charge induced in the capacitor?
(c) What is the maxium current that flows in the inductor?
(d) After two seconds after the switch turning into b, what is
the total energy of this circuit?
8. (10 pt) Two inductors L1 and L2 are connected in parallel and separated
by a large distance so that the magnetic field of one cannot affect the other.
(a) Show that the equivalent inductance is given by L=L1 + L2.
(b) If the two coils are now connected as in the Fig. and their mutual
inductance is M, show that this combination can be replaced by a single
coil of equivalent inductance given by Leq=L1+L2+2M.
(c) How could the coils be reconnected to yield an equivalent inductance of
Leq=L1+L2-2M.
9. (10 pt) In the figure shown, (a) determine the magnetic flux through
the loop due to the current i. (b) find the mutual inductance for the
loop-wire combination if N=100, a=1.0 cm, b=8.0 cm, and l=30 cm?
(c) Suppose the current is changing with a time, as di/dt=10.0 (A/s).
Find the direction and magnitude of the induced emf.
10. (10 pt) The figure in the right shows a cross section of a long conducting
coaxial cable and give its radii (a, b, c). Equal but opposite current i are
uniformly distributed in the two conductors. Derive expressions for B(r)
with radial distance in the ranges; (a) r<c (b) c<r<b, (c) b<r<a, and (d)
r>a (e) Obtain the total energy per unit length of the cable stored in the
space between the conductors, i.e., c<r<b.