 Physics
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Proficiency Exams |
| Physics Courses Faculty Research Events | P122 Exams |
1. (20) Two free point charges +q and +4q are a distance L apart. A third charge is placed so that the entire system is in (unstable) equilibrium. Find the location, magnitude and sign of the third charge.
2. (30) A spherical shell of inner radius a and outer radius b contains a charge per unit volume RHO = A/r where A is a constant. At the center of the shell, r = 0, there is a point charge q. What value of the constant A will cause the electric field in the region a<r<b to be constant in magnitude?
3. (25) A spherical drop of water carrying a charge of 30 pC has a potential of 500 V at its surface.
A. What is the radius of the drop?
B. If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop so formed?
4. (25) Aparallel plate capacitor has plates of area A and separation d and is charged to a potential difference V. The charging battery is then disconnected and the plates are pulled apart until their separation is 2d. Derive expressions in terms of A, d and V for
A. the new potential difference
B. the initial and final stored energy
C. the work required to separate the plates
5. (25) Assume that the batteries in the figure have negligible internal resistance. Find:
A. the current in the circuit
B. the power dissipated by each resistor
C. the power supplied or adsorbed by each battery.
6. (25) A 10 keV electron moving horizontally enters a region of space in which there is a downward-directed electric field of magnitude 10 kV/m.
A. What are the magnitude and direction of the (smallest) magnetic field that will allow the electron to continue to move horizontally? (Ignore gravity which produces relatively small forces.)
B. Is it possible for a proton to pass through this combination of fields undeflected? If so, under what circumstances?
7. (20) Consider the circuit shown to the right. The curved segments are arcs of circles of radii a and b. The straight segments are along the radii. Find the magnetic field B (including direction) at P, assuming a current in the circuit.
8. (30) Two parallel loops of wire have a common axis. The smaller loop of radius r is above the larger loop (radius R) by a distance x >>R (which is not shown accurately in the figure). Consequently the magnetic field due to the current i in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at a constant rate v = dx/dt.
A Determine the magnetic flux across the area bounded by the smaller loop as a function of x.