102 PHYS General Physics II
Final Exam, May 29, 2008 Duration: 130 minutes
I pledge, on my Honor, not to lie, cheat, or steal in either my academic or personal life. I understand that such acts violate the Honor Code and undermine the community of trust of which we are all stewards.
Signature: Name: Section:
Q.1 (25)
Q.2 (25)
Q.3 (25)
Q.4 (25)
Total (100)
Note: Solutions will be available after the exam at http://www.fen.bilkent.edu.tr/~phys102
Q.1 (25 points) Electrostatics
An infinitely-long nonconducting cylinder of radius R carries a nonuniform volume charge r density ! (r ) = !0 , where !0 is a known constant and r is the cylindrical radial R R distance from its axis (see the figure).
a) Using Gauss law determine the electric field vector everywhere (i.e., r<R
and r>R), b) Determine the corresponding electric potential everywhere, choosing V(a)=0, i.e., potential reference chosen at r=a where a>R. c) Can you choose infinity as potential reference? Give your reasoning.
r
(r)
Q.2 (25 points) Magnetic Field
Consider an infinite cylindrical wire of radius a centered along the z-axis with current density r J = z J 0 , where J0 is a constant which is known.
(a) Draw the direction of the magnetic field vector inside and outside of the wire. (No
calculation is required for this part.) (b) Determine the total current that passes through this wire. What (c) is the strength of the magnetic field inside the wire (as a function of the radial distance r from the wire axis)? (d) What is the strength of the magnetic field outside the wire (as a function of the radial distance r from the wire axis)? (e) Using parts ((c) and (d) plot magnetic field magnitude versus radial distance (B(r)) curve.
Q.3 (25 points) RL Circuits
In the figure, the switch is kept closed for t < 0, and steadystate conditions are established. At t = 0 the switch is opened. (a) Find the initial voltage VL across the inductor L just after t = 0. (b) Which end of the coil is at the higher potential: a or b? (c) Plot the currents in R1 and in R2 as a function of time, treating the steady-state directions as positive. Show values before and after t = 0. (d) How long after t =0 does the current in R2 have the 1/5 of its initial value?
Q.4 (25 points) Various topics
Give very brief (a couple of lines) answers for the following questions (5 points each) a) What is the difference between the magnetic behavior of a diamagnetic and a paramagnetic material? b) What does the Lenz law state? c) What is the frequency of (i) visible light, (ii) typical microwave oven, (iii) FM radio station? Order of magnitude estimates are sufficient. d) What is the SI unit for magnetic permeability? v e) Why should " B !nda vanish for any closed surface S? Explain.
S