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Supplementary Problems for PHYS 241 Test 2: Electric Potential and Capacitance - Prof. Dav, Exams of Physics

A set of supplementary problems for phys 241 test 2, covering topics on electric potential, electric fields, and capacitance. Students are asked to find electric field lines and equipotential lines for a point charge, calculate the electric potential and kinetic energy of an electron, find the electric field intensity using potential difference, determine the capacitance and energy stored in a capacitor, and find the equivalent capacitance and charges on capacitors in a network.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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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
pf2

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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.)

  1. 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?

  1. 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 = -d V /d x to find the x -component of the electric field intensity on the x -axis when x = 2.0 m.

  1. 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?

  1. 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

  1. Each of the capacitors in Figure 2 has a capacitance of 1.5 F.

a. Find the equivalent capacitance of the network between the

terminals a and b.

b. Suppose that the terminals a and b have a potential difference

of 50 v. Find the charge stored on each capacitor and the voltage

drop across each capacitor.

Answers to Supplementary Problems for PHYS 241

Test 2

  1. a. See your text for help.

b. See your text for help.

c.

0

Q 5 5

4 5D

  1. a. 150 eV = 2.4 x 10

    J 

b. 7.2 x 10

6 m/s

  1. 1.0 x 10

2 V/m

Figure

  1. a. 0.040 F

b. 18 J

  1. a. 5.6 cm

2

b. 3.0 pF

c. 9.0 nC (What happens if more charge than this is placed on the

capacitor?)

  1. a. 0.90 F

b. q 1 = 15 C, V 1 = 10 v

q 2

= 15 C, V

2 = 10 v

q 3 = 30 C, V 3 = 20 v

q 4 = 45 C, V 4 = 30 v