Physics 272. Final Exam

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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:




(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 tex2html_wrap_inline82 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 tex2html_wrap_inline86 ( tex2html_wrap_inline88 ) 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 tex2html_wrap_inline92 .

(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 tex2html_wrap_inline96 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 tex2html_wrap_inline100 .

(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 tex2html_wrap_inline102 , where tex2html_wrap_inline104 , an 50 mH inductor, a tex2html_wrap_inline106 F capacitor, and a 20 tex2html_wrap_inline108 resistor.

(a) Draw a circuit diagram for this circuit.
(b) What is the impedance for this circuit ?
(c) At what frequency tex2html_wrap_inline110 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 tex2html_wrap_inline112 Hz, the frequency for blue light is tex2html_wrap_inline114 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 ?

Tom Browder
Thu Jan 15 13:57:52 HST 1998