Physics 106 Homework Problems, Fall 2005

These problems are adapted from Serway and Faughn, College Physics, and are usedwith permission from Harcourt Brace College Publishers.

1-1. A 4.51-nC charge is located [01] m from a 2.86-nC charge. Find themagnitude of the electrostatic force exerted by one charge on the other.

1-2. In the figure, q1 = 6.27 C, q2 = [02] C,

q3 = 2.38 C, r1 = 3.49 cm, and r2 = 3.22 cm.Calculate the magnitude and direction of the Coulomb

force on (a) q1, (b) q2, and (c) q3. Indicate a force to

the right with a + sign and a force to the left with a sign.

1-3. Three charges are arranged as shown in the figure. Find the

(a) magnitude and (b) direction (angle with the x axis) of the

electrostatic force on the 6.00-nC charge. In the figure,

q = [03] nC.

1-4. Two small metallic spheres, each of mass 0.20 g, are suspended

as pendulums by light strings from a common point as shown

in the figure. The spheres are given the same electric charge,

and it is found that the two come to equilibrium when each

string is at an angle of [04] with the vertical. If

each string is 30.0 cm long, what is the magnitude of the

charge on each sphere?

2-1. (a) Determine the electric field at a point [01] cm to the left of the middle

charge shown in the figure. Use a plus sign for a field pointing to the right, and use a

minus sign for a field pointing to the left. (b) If a charge of 2.00 C is placed at thispoint, find the force acting on it. Use a plus sign for a force pointing to the right, and use

a minus sign for a force pointing to the left.

2-2. An electron is accelerated by a constant electric field of magnitude [02] N/C.

(a) Find the acceleration of the electron. (b) Use the equations of motion with constant

acceleration to find the electrons speed after 1.54 108 s, assuming it starts from rest.

2-3. Positive charges are situated at three corners of a

rectangle, as shown in the figure. Find the

(a) magnitude and (b) direction (angle with the

horizontal direction to the right) of the electric field at

the fourth corner. In the figure, d = [03] m.

3-1. A proton moves [01] cm parallel to a uniform electric field with E = 223 N/C.

(a) How much work is done by the field on the proton? (b) What change occurs in the

potential energy of the proton? (c) Through what potential difference did the proton

move?

3-2. Suppose an electron is released from rest in a uniform electric field whose strength is

[02] V/m. (a) Through what potential difference will it have passed after

moving 1.34 cm? (b) How fast will the electron be moving after it has traveled 1.34 cm?

3-3. Find the potential at point P for the rectangular grouping of

charges shown in the figure, where d = [03] m.

3-4. Two point charges are on the y axis. One charge of 3.18 nC is at the origin and a second

charge of 6.35 nC is at the point y = 29.2 cm. Calculate the potential at

y = [04] cm.

4-1. An air-filled capacitor consists of two parallel plates, each with an area of 7.65 cm2,

separated by a distance of [01] mm. If a 23.2-V potential difference is applied

to these plates, calculate (a) the electric field between the plates, (b) the capacitance,

and (c) the magnitude of the charge on each plate.

4-2. A series circuit consists of a 0.056-F capacitor, a [02] -F capacitor, and a

400-V battery. Find the charge on (a) the first capacitor and (b) the second capacitor. If

the capacitors are reconnected in parallel across the battery, find the charge on (c) the

first capacitor and (d) the second capacitor.

4-3. Consider the combination of capacitors in the

figure, where C = [03] F and

V = [04] V. (a) What is the

equivalent capacitance of the group? Determine

the charge on (b) the 4.00-F capacitor, (c) the

2.00-F capacitor, (d) the 24.0-F capacitor, and

(e) the capacitor C.

4-4. A [05] -F capacitor (C1) is first charged by being connected across a 10.0-V

battery. It is then disconnected from the battery and connected across an uncharged

2.27-F capacitor (C2). Determine the resulting charge on (a) C1 and (b) C2.

5-1. In a particular television picture tube, the measured beam current is [01] A.

How many electrons strike the screen every second?

5-2. A potential difference of 12 V is found to produce a current of [02] A in a

3.2-m length of wire with a uniform radius of 0.43 cm. What is (a) the resistance of the

wire and (b) the resistivity of the wire?

5-3. A toaster is rated at [03] W when connected to a 120-V source. (a) What

current does the toaster carry, and (b) what is its resistance?

5-4. A high-voltage transmission-line with a resistance of [04] /km carries

1460 A, starting at 701 kV for a distance of 168 km. (a) What is the power loss due to

resistance in the line? (b) What percentage of the transmitted power does this loss

represent?

6-1. Three resisters are connected in series with a 24-V battery. Their resistances are

R1 = 4.00 , R2 = [01] , and R3 = 12.00 . (a) Find the equivalent

resistance. Find the current in (b) R1, (c) R2, and (d) R3. (e) Find the equivalent

resistance if the three resisters are connected in parallel across the battery. Find the

current in (f) R1, (g) R2, and (h) R3 for this case.

6-2. (a) Find the equivalent resistance between points a and b in

the figure, where R = [02] . (b) Calculate the

current in the resister R if a potential difference of 34.0 V is

applied between points a and b.

6-3. Find the current in the 12- resistor in the figure,

where R = [03] .

6-4. If R = [04] in the figure, find the current in

the (a) top, (b) middle, and (c) bottom resistors. The

algebra in this problem is challenging. Apply the loop rule

to the top loop first and then to the bottom loop.

6-5. Extra credit activity: Connecting a light bulb to a battery. For this activity, you will

need (1) a 1.5-V battery (the kind which is in a flashlight or in your quiz transmitter),

(2) a small lightbulb (handed out in class, or, if you didnt get one in class, remove one

from a flashlight), and (3) a wire about 6 inches long (or anything metallic, such as a

strip of aluminum foil). Connect these three items together so that the lightbulb turns

on. When you submit your homework answers, select yes if you were able to turn on

the light bulb and select no if not.

7-1. Find the equivalent resistance between points a and b

in the figure if R = [01] .

7-2. Find the values of (a) I1, (b) I2, and (c) I3 for the

circuit in the figure if R = [02] . The

algebra in this problem is challenging. Apply the loop

rule to the outer loop first and then to the left loop.

7-3. An uncharged capacitor and a resistor are connected in series to a source of emf. If

E = 9.00 V, C = [03] F, and R = 127 , find (a) the time constant of the

circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor

after one time constant.

7-4. Consider the circuit shown in the figure, where R = [04] k and

C = [05] F. Suppose that the switch has been closed for a length of time

sufficiently long for the capacitor to become fully charged. Find the steady-state current

in (a) the 12.0-k resistor, (b) the resistor R, and (c) the 3.00-k resistor. (d) Find the

charge on the capacitor.

8-1. Find the direction of the force on a

proton (a positively charged

particle) moving through the

magnetic fields in the figure, as

shown. In each case, give one of the

following answers: toward top of

page, toward bottom of page, to the

right, to the left, out of page, into

page.

8-2. A wire carries a steady current of [01] A. A straight section of the wire is

0.752 m long and lies along the x axis within a uniform magnetic field of magnitude

1.68 T in the positive z direction. If the current is in the +x direction, what is the

(a) magnitude and (b) direction of the magnetic force on the section of wire?

8-3. A circular coil consisting of a single loop of wire has a radius of 28.6 cm and carries a

current of 25.4 A. It is placed in an external magnetic field of 0.293 T. Find the torque

on the wire when the plane of the coil makes an angle of [02] with the

direction of the field.

9-1. A 2.53-C charged particle with a kinetic energy of 0.0929 J is fired into a uniform

magnetic field of magnitude 0.147 T. If the particle moves in a circular path of radius

[01] m, determine its mass.

9-2. The two wires in the figure carry currents of I1 = [02] A

and I2 = [03] A, in a direction out of the page as shown.

Find the (a) magnitude and (b) direction of the magnetic field at a

point midway between the wires. Find the (c) magnitude and

(d) direction of the magnetic field at point P , located 20.0 cm

above the wire carrying the current I2.

9-3. Find the direction of the current in the

wire in the figure that would produce a

magnetic field directed as shown, in each

case. (a) Answer to the right or to the

left. (b) Answer into or out of the page.

9-4. Two parallel wires are 12.3 cm apart, and each carries a current of [04] A.

(a) If the currents are in the same direction, find the force per unit length exerted by one

of the wires on the other. (b) Are the wires attracted or repelled?

10-1. A solenoid 4.29 cm in diamete