**Physics 272. Final Exam**

**Please write your name at the top of the page**

**There are 8 problems. Each is assigned 25 points.**

**Show your work.**

Problem 1: 25 points

A solid insulating sphere of radius R
carries a **non-uniform** charge density:

and

(a) What is the magnitude of the electric field
inside the sphere ?

(b) What is the magnitude of the electric field
outside the sphere ?

(c) Is the electric field in the *radial*,
*tangential*, or * direction* ?

Problem 2: 25 points

The wire semicircles have radii a and b. A current I is flowing
in the wire.
(a) Find the magnitude of the magnetic field at point P.

(b) Find the direction of the magnetic field at point P.

Problem 3: 25 points

A solenoid of radius *r* and length ( )
is uniformly wound with *n* turns.
A square coil of side length a and N turns is placed around
it, near its center. The current in the solenoid is changing at
a rate of .

(a) What is the current induced in the resistance R ?
(Hint: remember the B field outside the solenoid is zero).

(b) If the current in the solenoid changes from 0 to
what is the charge q that flows through the circuit ?
(Hint: how is charge related to current ?)

Problem 4: 25 points

A straight solenoid of diameter 5 cm and length 25 cm is wrapped
with 200 turns of wire. The solenoid carries a current *I* = 5A.
The solenoid is filled with a material of magnetic susceptibility
.

(a) What is the magnetic field inside the solenoid ?

(b) By what factor has the magnetic field changed due
to the presence of the material ?

(c) Was the material used to fill the solenoid a
*diamagnetic substance*, a *paramagnetic substance*,
a *ferromagnetic substance*, or a *superconductor* ?
(give a short qualitative explanation for your answer).

Problem 5: 25 points

A series AC circuit consists of three components: an EMF source with , where , an 50 mH inductor, a F capacitor, and a 20 resistor.

(a) Draw a circuit diagram for this circuit.

(b) What is the impedance for this circuit ?

(c) At what frequency will the power
dissipated in the resistor be the largest ?

Problem 6: 25 points

A demonstration laser has an average output power of 0.9 mW and a beam diameter of 1.2 mm.

(a) What is the force exerted by the laser beam
on a perfectly reflecting surface ?

(b) Is this force much *larger*, *smaller*,
or about the same size as other forces present in daily life
(wind, seismic noise, etc..) ?

Problem 7: 25 points

A collimated beam of white light is incident on a prism of fused quartz as shown. A plot of the index of refraction for quartz versus wavelength is given.

(a) The frequency for red light is Hz,
the frequency for blue light is Hz, what are
the wavelengths for red and blue light ?

(b) Calculate the angle between the emerging beams of red
and blue light.

Problem 8: 25 points

A converging lens has a focal length of 20 cm. A candle is located 50 cm from the lens.

(a) Draw a simple diagram of this setup showing the position
of the object, lens, and image.

(b) Where is the image located relative to the object ?

(c) By what factor is the image magnified ?

(d) Is the image *inverted*, *erect*
*sideways*, or *inside out* ?

Thu Jan 15 13:57:52 HST 1998