Supplementary Problems for PHYS 241
Test 2
1. Consider a point charge Q a distance D from an infinite conducting plane
connected to ground, as shown in Figure 1. (Assume that Q is a positive
charge.)
a. Draw several electric field lines from Q to the conducting plane. (Remember
what angle the field lines must make with the conducting surface when they
intersect the surface.) (Make the electric field lines solid; use arrowheads
to show the direction of the electric field.)
b. In the same drawing you made in part a draw several equipotential lines. (Make the equipotential lines
dashed.)
c. Find the electric potential at a point a distance D directly above the point charge Q. (Hint: Replace the
infinite plane with an image charge -Q that sits a distance D behind the plane directly opposite Q.)
2. An electron, initially at rest, leaves a cathode that is maintained at a potential of -50 v and strikes an anode
maintained at a potential of +100 v.
a. Find the kinetic energy of the electron when it strikes the anode. Express your answer in eV and in
joules.
b. What is the electron's speed when it strikes the anode?
3. The electric potential along the x-axis is given by V = (90/x) + [40/(x - 1)2] (x in meters, V in volts).
Use E = -dV/dx to find the x-component of the electric field intensity on the x-axis when x = 2.0 m.
4. A capacitor stores a charge of 1.8 C when the potential difference across its plates is 45 volts.
a. What is the capacitance of this capacitor?
b. If the potential difference across the plates of this capacitor is 30 volts, how much electrical potential
energy does it store?
5. An air capacitor has capacitance 2.5 pF; the separation between its plates is 2.0 mm.
a. What is the area of each of the capacitor's plates?
b. A dielectric with dielectric constant 1.2 is placed between the plates of the capacitor so that it completely
fills the gap between the plates. What is the new capacitance of the capacitor?
c. If the dielectric strength of the dielectric is 1500 v/mm, what is the maximum charge that can be placed on
the capacitor? What happens to the capacitor if more than this maximum charge is placed on it?
Continued on the other side
D
Q
Figure 1
