## Physics II Homework Page

##### Homework Page with Visable Answers

This page has all of the homework for the second semester of College Physics. You can go directly to each section using the links above or by using the menu.

#### Charge and Current

1. A current of 10 A flows for 10 sec. How much charge does that represent?
100 Coul
2. A 12 Coul charge flows for 60 sec, what is the current?
0.2 A
3. How long must a 6 Coul charge flow to create a current of 3 A?
2 sec
4. #### Coulomb's Law

5. A 3 Coul charge and a 2 Coul charge are separated by 0.3 m. What is the force between them?

F = (k)(q1)(q2)/r² = [(9 x 109 N-m²/Coul²)(2 Coul)(3 Coul)]/(0.3 m)²

F = 6 x 1011 N

6. The force between two charges is 3.5 N. If the charges are 1.2 m apart and one charge is 3.4 Coul, what is the second charge?

q2 = (F)(r²)/(k)(q1) = (3.5 N)[(1.2 m)²]/[(9 x 109 N-m²)(3.4 Coul)]

q2 = 1.65 x 10-10 Coul

7. Two identical charges are 40 cm apart. What are the charges if the force between them is 1.2 N?

q² = (F)(r²)/(k) = (1.2 N)[(0.4 m)²]/(9 x 109 N-m²)

q = 4.62 x 10-6 Coul

8. Two pith balls, each with a mass of 2 x 10-5 kg, have identical charges and are suspended from a point by two light strings. The charges cause the balls to repel, which results in an angle of 5° between the two strings. What is the charge on each of the pith balls?
9. #### Electric Field

10. What is the electric field strength produced by a 1.8 Coul charge that is 1.5 m away?

E = (k)(q)/r² = (9 x 109 N-m²/Coul²)(1.8 Coul)/(1.5 m)² = 7.2 x 108 N/Coul

11. What is the electric field strength 2.5 m from a -1.8 Coul charge?

E = (k)(q)/r² = (9 x 109 N-m²/Coul²)(-1.8 Coul)/(2.5 m)²

E = -2.59 x 109 N/Coul

12. A 3.0 Coul charge is at 4.5 m on the x-axis, and a second 4.5 Coul charge is at 2.0 m on the y-axis. What is the magnitude and dirction of the electric field at the origin?
13. #### Electric Potential

14. What is the electric potential produced by a 1.8 Coul charge that is 1.5 m away?

V = (k)(q)/r = (9 x 109 N-m²/Coul²)(1.8 Coul)/(1.5 m)

E = 1.08 x 1010 V

15. What is the electric potential 2.5 m from a -1.8 Coul charge?

V = (k)(q)/r = (9 x 109 N-m²/Coul²)(-1.8 Coul)/(2.5 m)

E = -6.48 x 109 V

16. A 3.0 Coul charge is at 4.5 m on the x-axis, and a second 4.5 Coul charge is at 2.0 m on the y-axis. What is the magnitude of the electric potential at the origin?

V = (k)(q)/r; V = V1 + V2

V = (9 x 109 N-m²/Coul²)(3 Coul)/(4.5 m) + (9 x 109 N-m²/Coul²)(4.5 Coul)/(2.5 m)

E = 6 x 109 + 1.6 x 1010 = 2.22 x 1010 V

17. #### Electric Field and Electric Potential

18. Three charges, q1, q2, q3, form an equilateral triangle with sides 2.5 m. If q1 = 1 Coul, q2 = 2 Coul, and q3 = 4 Coul, (a) what is the magnitude and direction of the electric field strength at the center of the triangle? (b) What is the potential that the center of the triangle?
19. Charges are positioned at the corners of a square having sides equal to 2 cm. On three of the corners the charge is 3 Coul, on the other corner the charge is -3 Coul. Find the field and potential at the center of the square.
20. Charges are positioned at the corners of a square having sides equal to 2 cm. On three of the corners the charge is 3 Coul, on the other corner the charge is -3 Coul. Find the field and potential along one side of the square that is half way between two of the 3 Coul charges on that side of the square.
21. #### Capacitors

22. A capacitor whose capacitance is 15 µF is momentarily connected to a dry cell that maintains a potential difference of 1.2 V between its terminals. It is disconnected. How much charge is stored in the capacitor?

q = (C)(V) = (15 x 10-6 F)(1.2 V) = 1.8 x 10-5 Coul

23. A 20 µF air capacitor is connected to a 5 V battery and then removed from the battery. The capacitor is then submerged in an oil with K = 3.5. What is the energy stored in the capacitor (a) before and (b) after submersion in the oil? [Answer: (a) 250 µJ; (b) 71.4 µJ]

#### Resistivity, Ohm's Law, Power, and Energy

1. What is the resistivity of a resistor that is 0.5 cm long and has a cross-sectional area of 0.002 m² and a resistance of 1.5 Ω?

ρ = R(A/L) = (1.5 Ω)(0.002 m²)/(0.005 m) = 0.6 Ω-m

2. What is the cross-sectional area of a 300 Ω resistor that is 1.0 cm long and made of carbon (ρ = 4 x 10-5)?

A = (ρ)(L)/R = (4 x 10-5 Ω-m)(0.001 m)/(300 Ω) = 1.3 x 10-10

3. A 6 V battery is connected in a circuit with a resistance of 2 Ω. What is the current in this circuit?

I = V/R = (6 V)/(2 Ω) = 3 A

4. (a) How much potential is produced by a 2 A current through a 32 Ω resistor? (b) How much power is used by the resistor?

V = IR = (2 A)(32 Ω) = 64 V

P = I²R = (2 A)²(32 Ω) = 128 W

5. (a) What is the current going through a 45 Ω resistor that has a potential of 5 V? (b) How much power is used by the resistor?

I = V/R = (5 V)/(45 Ω) = 0.11 A

P = V²/R = (5 V)²/(45 Ω) = 0.56 W

6. (a) What is the resistance of a resistor that has a potential of 3 V with a current of 9 A? (b) How much power is used by the resistor?

R = V/I = (3 V)/(9 A) = 0.33 Ω

P = VI = (3 V)(9 A) = 27 W

7. How much current does a 60 W lamp have when connected to a 120 V power supply?

I = P/V = (60 W)/(120 V) = 0.5 A

8. (a) How much energy does a 60 W lamp use in 1.0 hour? (b) How much energy does a 100 W lamp use in 1.0 hour?

E = Pt = (60 W)(3600 sec) = 216 kJ

E = Pt = (100 W)(3600 sec) = 360 kJ

9. (a) How much energy is used by a toaster that is on for 2.0 minutes if it draws 7.5 A at 120 V? (b) What is the resistance of this toaster?

E = Pt = VIt = (120 V)(7.5 A)(120 sec) = 108 kJ

R = V/I = (120 V)/(7.5 A) = 16 Ω

10. A certain fluorescent lamp draws 0.33 A at 120 V. (a) What is its resistance? (b) How much power does it require? (c) How many Joules of energy are used in 3.0 minutes?

R = V/I = (120 V)/(0.33 A) = 364 Ω

P = VI = (120 V)(0.33 A) = 39.6 W

E = Pt = VIt = (120 V)(0.33 A)(180 sec) = 7128 J

11. A certain 60 W tungsten filament lamp has a resistance of 240 Ω when it is lit (the temperature is about 2000 °C). (a) What is the voltage across the filament? (b) What is the current through the filament? (c) How many Joules of energy are used in 3.0 minutes?

V = [(P)(R)]½ = [(60 W)(240 Ω)]½ = 120 V

I = V/R = (120 V)/(240 Ω) = 0.5 A

E = Pt = (60 W)(180 sec) = 10.8 kJ

1. Three identical resistors are combined in series and have an equivalent resistance of 12 Ω. What is the resistance of each of the resistors?

Rs = R1 + R2 + R3 = 3R     R = (12 Ω)/3 = 4 Ω

2. Three identical resistors are combined in parallel and have an equivalent resistance of 0.6667 Ω. What is the resistance of each of the resistors?

1/Rp = 1/R1 + 1/R2 + 1/R3 = 3/R     R = (3)(0.667 Ω) = 2 Ω

3. Three resistors are available: 2 Ω, 4 Ω, and 6 Ω. (a) How can the three resistors be combined to give an equivalent resistance of 3 Ω? (b) How can the three resistors be combined to give an equivalent resistance of 12 Ω? (c) How can the three resistors be combined to give an equivalent resistance of 1.09 Ω? (d) How can the three resistors be combined to give an equivalent resistance of 4.4 Ω?

#### Electrical Circuits

1. Find I2, I3, and I4 shown below. (6 A, 3 A, 9 A)
2. Find I1, I2, and I3 shown below. (3 A, 3 A, 6 A)
3. Find the current through the 5, 6, and 12 Ω resistors shown below. (9 A, 6 A, 3 A)
4. Find the current, I, through the battery shown below when the battery has an EMF, E, of 36 V and an internal resistance, r, of 2 Ω, and each resistor has a resistance of 10 Ω. (2 A, the equivalent resistance is 8 Ω)
5. (a) Find the resistance and voltage across the unknown resistor labeled R. (4 V, 0.667 Ω) (b) How much power is generated by the battery? (80 W)
6. #### Solving for Currents Using the Matrix Method

7. Find I1, I2, and I3 shown below using the matrix method. (1.31 A, 0.846 A, 0.462 A)
8. Find I1, I2, and I3 shown below using the matrix method. (3 A, 5 A, 2 A)
9. #### Meters

10. What shunt resistance is needed to make a 15 A ammeter with a galvanometer that has a maximum current of 0.0001 A and a resistance of 150 Ω?
11. What multiplier resistance is needed to make a 150 V voltmeter with a galvanometer that has a maximum current of 0.0001 A and a resistance of 150 Ω?
12. (a) Show how an ammeter could be constructed to read 5 A full scale. (b) Show how a voltmeter could be constructed that reads 50 V full scale. Use a galvanometer that needs 1.5 mA for full-scale deflection and has an internal resistance of 200 Ω.

#### Magnetism

1. What is the magnitude and direction of the magnetic force when a current of 2 A travels toward the north through a north-south horizontal wire that is 40 m long and through a downward perpendicular B-field of 0.1 T?

Fmag = (I)(ΔL)(B) = (2 A)(40 m)(0.1 T) = 8 N, toward the West

2. What is the magnitude and direction of the magnetic force when a current of 2 A travels toward the north through a north-south horizontal wire that is 40 m long and through a horizontal B-field of 0.4 T that is at an angle of 30° toward the north from east (the B-field goes from the south-west to the north-east)?

Fmag = (I)(ΔL)(B) = (2 A)(40 m)(0.4 T)(cos 30°) = 27.7 N, Downward

3. What is the magnitude and direction of the perpendicular B-field when a current of 2 A travels through a wire that is 40 m long with a resulting force of 5 N to the west?

B = Fmag/[(I)(ΔL)] = (5 N)/[(2 A)(40 m)] = 0.0625 T, Downward

4. What current is needed along a 100 m wire to have a 3 N magnetic force in a perpendicular B-field of 2 T?

I = Fmag/[(ΔL)(B)] = (3 N)/[(100 m)(2 T)] = 0.015 T

5. How long does a wire have to be to have 4 N of magnetic force from a 6 T perpendicular magnetic field with a current of 1.5 A?

ΔL = Fmag/[(I)(B)] = (4 N)/[(1.5 A)(6 T)] = 0.444 m

6. What is the magnitude of the magnetic force when an electron (q = 1.6 x 10-19 Coul) travels with a speed of 2 x 108 m/sec in a perpendicular B-field of 0.0002 T?

Fmag = qVB = (1.6 x 10-19 Coul)(2 x 108 m/sec)(0.0002 T)] = 6.4 x 10-15 N

7. What is the magnitude and direction of a B-field that keeps an electron traveling horizontally toward the north at the speed of light? The mass of an electron is 9.11 x 10-31 kg, the charge of an electron is 1.6 x 10-19 Coul, and the speed of light is 3 x 108 m/sec. (1.9 x 10-19 T toward the east)
8. If a current of 2.4 A goes clockwise in a loop that has a radius of 0.5 m, what is the B-field at the center of the loop?

Bloop = 2πIk/r = (2)(3.142)(2.4 A)(10-7 N/A²)/(0.5 m) = 3.02 x 10-6

9. Three long vertical wires, A, B, and C, are lined up parallel to each other in the same plane with wire B in the middle. If wire A is 0.1 m from wire B with 2 A going upward and wire C is 0.15 m from wire B with 3 A going upward, what is the magnitude and direction of the current in the center wire (wire B)? (1.2 A, downward)
10. Three long vertical wires, A, B, and C, are lined up parallel to each other in the same plane with wire B in the middle. If wire A is 0.3 m from wire B with 1.2 A going upward and wire C is 0.4 m from wire B with 1.6 A going upward, what is the magnitude and direction of the current in the center wire (wire B)? (0.686 A, downward)
11. Three long vertical wires, A, B, and C, are lined up parallel to each other in the same plane with wire B in the middle. If wire A is 1.2 m from wire B with 4.5 A going upward and wire C is 0.8 m from wire B with 3.0 A going upward, what is the magnitude and direction of the current in the center wire (wire B)? (1.8 A, downward)
12. A square loop of wire 3 cm on an edge is lying on a horizontal table. An electromagnet above and to one side of the loop is turned on, causing a uniform magnetic field that is downward at an angle of 25° from the vertical. The magnetic induction is 0.07 T (or 0.07 Wb/m²). Calculate the average induced EMF in the loop if the field increases from zero to its final value in 150 msec.

Φ = BA = (0.07 Wb/m²)(cos 25)(0.04 m)² = 1.02 x 10-4 Wb

E = ΔΦ/Δt = (1.02 x 10-4 Wb)/(0.15 sec) = 6.77 x 10-4 V

13. #### Extra Magnetism Problems

14. What is the magnitude and direction of a B-field that keeps a proton traveling horizontally toward the north at the speed of light?
15. What velocity must an electron have to keep it traveling horizontally through a perpendicular horizontal magnetic field of 6 x 10-6 T?
16. What charge must a particle with four time the mass of a proton have to keep it traveling horizontally through a perpendicular, horizontal magnetic field of 6 x 10-6 T?
17. What velocity must an electron have to keep it traveling horizontally through a magnetic field of 6 x 10-6 T that is 60° from horizontal?
18. What charge must a particle with four times the mass of a proton have to keep it traveling horizontally through a magnetic field of 6 x 10-6 T that is directed 60° from horizontal?
19. If a current of 3.2 A goes clockwise in a loop that has a radius of 0.75 m, what is the B-field at the center of the loop?
20. Circular loop A, with a radius of 0.5 m and current of 2.4 A, is placed so that its center is at the center of circular loop B, which has a radius of 0.75 m and a current of 3.2 A. Both loops are in the same plane. What is the magnitude and direction of the B-field at the center of the loops?

#### Nuclear Physics

1. The mass of 13N is 13.005739 u. What is the total binding energy of this nuclide? The mass of a proton is 1.0072 u and the mass of a neutron is 1.0087 u.

Mass Difference = (7)(1.0072 u) + (6)(1.0087 u) - 13.005739 u = 0.096861 u

Binding Energy = (931 MeV/u)(0.096861 u) = 90.2 MeV

2. Calculate the energy released in the β+ decay of 64Cu. The masses of 64Cu and 64Ni are 63.929766 u and 63.927968 u, respectively.
3. Write nuclear equations for the following reactions: (a) β- decay of 90Sr, (b) β+ decay of 40K, (c) electron capture by 22Na, (d) α-decay of 210Po.
4. (a) Write the radioactive decay series for 211Pb. (b) Write the radioactive decay series for 47K. (c) Write the radioactive decay series for 43Ti. (d) Write the radioactive decay series for 37Ca.
5. What are the initial activity, decay constant, and half-life of a nuclide that has an activity of 95 Ci after 6 seconds and an activity of 78 Ci after 12 seconds?
6. How long is required for 211Bi (t½ = 2.16 min) to lose one third of its activity?
7. Nuclei of 44K have a half-life of 22 minutes. (a) What is the decay constant for 44K? (b) What is the number of counts per minute after 1.0 hour if the initial count is 4567 counts/min?
8. How much time has elapsed if a sample has a half-life of 30 years, a current activity of 340 counts/min, and an initial activity of 950 counts/min?

#### Optics Problems

1. Light with a wavelength of 4 x 10-7 m enters one side of a glass prism (n = 1.5) from air (n = 1) at an angle of 30° from the normal. The prism is equilateral, with angles of 60°: at each corner. (a) What is the wavelength of the light in the glass? (b) At what angle from the normal to the initial surface will the light travel inside of the glass? (c) What angle will the light make with the normal to the seond surface? (d) At what angle will the light emerge from the prism? (e) Is there an angle of incidence from air that will cause total internal reflection to occur on the second surface? Answer
2. What is the index of refraction of a material that has an angle of incidence of 30° from the normal in air and an angle of 25° from the normal in the material?
3. What is the critical angle for a water (n = 1.333) and air (n = 1) interface?
4. An object 0.005 m high is placed 0.25 m from a double concave lens with a focal length of 0.06 m. (a) Where will the image appear? (b) Will the image ge inverted or erect? (c) Is the image real or virtual? (d) What size will the image be?
5. An object 0.008 m high is placed 0.15 m from a double convex lens with a focal length of 0.08 m. (a) Where will the image appear? (b) Will the image ge inverted or erect? (c) Is the image real or virtual? (d) What size will the image be?
6. An erect image 0.5 times larger than the object is observed at 0.03 m from a lens on the same side of the lens as the object. (a) Is the lens diverging or converging? (b) How far from the lens is the object? (c) What is the focal length of the lens?