Physics

Problem Set #6

NOTE: Any answers of zero must have some kind of justification. 1) You have a cylindrical metal shell of

inner radius 6 cm and outer radius 9 cm. The shell has no net charge. Inside the shell is a line of charge of linear density of – 7 μC/m. Find the magnitude and direction of the electric field at (a) r = 3 cm, (b) r = 7 cm, and (c) r = 13 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.

2) You have a uniformly charged

sphere of radius 5 cm and volume charge density of – 7 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has a net charge 8 μC. (a) Calculate the total charge on the sphere. Find the magnitude and direction of the electric field at (b) r = 13 cm and (c) r = 18 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.

3) Two 2 cm thick infinite slabs of metal are positioned as

shown in the diagram. Slab B has no net charge but Slab A has an excess charge of 5 μC for each square meter. The infinite plane at the origin has a surface charge density of – 8 μC/m2. Find the magnitude and direction of the electric field at (a) x = 2 cm, and (b) x = 4 cm. Also, calculate the surface charge density on (c) the left edge of A, (d) the right edge of A, and (e) the left edge of B.

4) A positive charge of 16 nC is nailed down with a #6 brad.

Point M is located 7 mm away from the charge and point G is 18 mm away. (a) Calculate the electric potential at Point M. (b) If you put a proton at point M, what electric potential energy does it have? (c) You release the

proton from rest and it moves to Point G. Through what potential difference does it move? (d) Determine the velocity of the proton at point G.

5)

All the charges above are multiples of “q” where

q = 1μC. The horizontal and vertical distances between the charges are 25 cm. Find the magnitude of the net electric potential at point P.

6) Use the same charge distribution as in problem #5 but

change all odd-multiple charges to the opposite sign. Find the magnitude of the net electric potential at point P.

7) A parallel plate setup has a distance

between the plates of 5 cm. An electron is place very near the negative plate and released from rest. By the time it reaches the positive plate it has a velocity of 8 x 106 m/s. (a) As the electron moves between the plates what is the net work done on the charge? (b) What is the potential difference that the electron moves through? (c) What is the magnitude and direction of the electric field in between the plates?

– 8q +9q

– 4q

A B

0 3 cm 5 cm 8 cm 10 cm

+9q

– 5q

+6q+6q

+2q

P

+ M G

8)

A uniform line of charge with density, λ, and length, L is positioned so that its left end is at the origin. See diagram above. (a) Determine an equation (using integration) for the magnitude of the total electric potential at point P a distance, d, away from the origin. (b) Calculate the magnitude of the electric potential at P if d = 2 m, L = 1 m, and λ = – 5 μC/m. c) Using the equation you derived in part a), calculate the equation for the electric field at point P. It should agree with the result we got in Lecture Example #19.

9) You have a thin spherical shell

of radius 10 cm with a uni- form surface charge density of 11 μC/m2. Centered inside the sphere is a point charge of – 4 μC. Using integration, find the magnitude of the total electric potential at: (a) r = 16 cm and (b) r = 7 cm.

10) You have a uniformly

charged sphere of radius 5 cm and volume charge density of 6 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has no net charge. Find the magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, and (c) r = 8 cm.

11) Use the same physical situation with the exception

of changing the inner sphere to a solid metal with a surface charge density of 9 μC/m2 and giving the shell a net charge of – 3 μC. Find magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, (c) r = 8 cm, and (d) r = 2 cm.

12) CSUF Staff Physicist & Sauvé Dude, Steve

Marley, designs a lab experiment that consists of a vertical rod with a fixed bead of charge Q = 1.25 x 10–6 C at the bottom. See diagram. Another bead that is free to slide on the rod without friction has a mass of 25 g and charge, q. Steve releases the movable bead from rest 95 cm above the fixed bead and it gets no closer than 12 cm to the fixed bead. (a) Calculate the charge, q, on the movable bead. Steve then pushes the movable bead down to 8 cm above Q. He releases it from rest. (b) What is the maximum height that the bead reaches?

13)

d

P

0 – – – – –

L

You have two metal spheres each of diameter 30 cm that are space 20 cm apart. One sphere has a net charge of 15 μC and the other – 15 μC. A proton is placed very close to the surface of the positive sphere and is release from rest. With what speed does it hit the other sphere?

14) A thin spherical shell of radius, R, is centered at the

origin. It has a surface charge density of 2.6 C/m2. A point in space is a distance, r, from the origin. The point in space has an electric potential of 200 V and an electric field strength of 150 V/m, both because of the sphere. (a) Explain why it is impossible for r < R. (b) Determine the radius, R, of the sphere.

15) The two charges above are fixed and cannot move. Find a

point in space where the total electric potential will equal zero.

ANSWERS:

Q

q

+

20 cm

+

6 cm

– – 4 μC 12 μC

6) – 7.87 x 104 V 7) a) 2.92 x 10-17 J

1) a) 4.20 x 106 N/C, I

b) 0 c) 9.68 x 105 N/C, I d) 1.86 x 10–5 C/m2 e) – 1.24 x 10–5 C/m2 2) a) – 3.67 x 10–6 C b) 0 c) 1.20 x 106 N/C, O d) 2.92 x 10–5 C/m2 e) 1.73 x 10–6 C/m2 3) a) 7.35 x 105 N/C, L

b) 0

b) 182.2 V c) 3644 N/C

8) a)   

   +λ

d Ldlnk

b) – 1.83 x 104 V 9) a) – 1.47 x 105 V b) – 3.90 x 105 V 10) a) 1.41 x 105 V b) 1.88 x 105 V c) 2.59 x 105 V 11) a) – 8.37 x 104 V b) – 1.12 x 105 V c) – 8.62 x 104 V d) – 9900 V 12) a) 2.48 x 10–6 C b) 1.42 m 13) 1.4 x 107 m/s 14) 2.86 m

c) 6.5 x 10–6 C/m2 d) – 1.5 x 10–6 C/m2 e) 1.5 x 10–6 C/m2 f) – 1.5 x 10–6 C/m2 4) a) 2.06 x 104 V b) 3.29 x 10–15 J c) – 1.26 x 104 V d) 4.91 x 105 m/s 5) 5.02 x 105 V 15) 1.5 cm

Physics 226 Fall 2013

Problem Set #7 1) You have a parallel plate capacitor of plate separation

0.1 mm that is filled with a dielectric of neoprene rubber. The area of each plate is 1.8 cm2. (a) Calculate the capacitance of the capacitor. The capacitor is charged by taking electrons from one plate and depositing them on the other plate. You repeat this process until the potential difference between the plates is 350 V. (b) How many electrons have been transferred in order to accomplish this?

2) A capacitor with ruby mica has an effective electric field

between the plates of 4600 V/m. The plates of the capacitor are separated by a distance of 4 mm. 50 mJ of energy is stored in the electric field. (a) What is the capacitance of the capacitor? (b) Calculate the energy density in between the plates.

3) A capacitor with a dielectric of paper is charged to 0.5 mC.

The plates of the capacitor are separated by a distance of 8 mm. 40 mJ of energy is stored in the electric field. (a) What is the strength of the effective electric field? (b) Calculate the energy density in between the plates.

4) A capacitor of 10 μF is charged by connecting it to a

battery of 20 V. The battery is removed and you pull the plates apart so that you triple the distance between them. How much work do you do to pull the plates apart?

5) The flash on a disposable camera contains a capacitor

of 65 μF. The capacitor has a charge of 0.6 m C stored on it. (a) Determine the energy that is used to produce a flash of light. (b) Assuming that the flash lasts for 6 ms, find the power of the flash. (Think back to 225.)

6) A spherical shell conductor of

radius B encloses another spherical shell conductor of radius A. They are charged with opposites signs but same magnitude, q. (a) Using integration, derive an equation for the capacitance of this spherical capacitor. (b) Calculate the capacitance if A = 45 mm and B = 50 mm. (c) If q = 40 μC, what is the energy density in between the shells?

7) You attach a battery of 15 V to an air-filled capacitor of 5 μF and let it charge up. (a) If the plate separation is 3 mm, what is the energy density in between the plates? You then remove the battery and attach the capacitor to a different uncharged capacitor of 2 μF. (b) What is the amount of charge on each capacitor after they come to equilibrium?

8) You attach a 100 pF capacitor to a battery of 10 V. You

attach a 250 pF to a battery of 7 V. You remove both of the batteries and attach the positive plate of one capacitor to the positive plate of the other. After they come to equilibrium, find the potential difference across each capacitor.

9) Do problem #8 but when you attach the capacitors

together attach the opposite sign plates instead of the same sign plates.

10)

Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.

11)

4 μF

4 μF

6 μF

12 μF

30 μF

20 μF

A

B

75 μF

6 μF

12 μF

12 μF

18 μF

20 μF

A

B

Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.

12) Design a circuit that has an equivalent capacitance of

1.50 μF using at least one of each of the following capacitors: a 1 μF, a 2 μF, and a 6 μF. [You must also show where your A and B terminals are located.]

13) The two capacitors above both have plates that are

squares of sides 3 cm. The plate separation is 1.2 cm for both. Between each of the capacitor plates are two different dielectrics of neoprene rubber and Bakelite. Everything is drawn to scale. Find the capacitance of each capacitor. (HINT: Think series and parallel.)

14) The plates of an air-filled capacitor have area, A, and are

separated by a distance, d. The capacitor is charged by a battery of voltage, V. Three things are going to change: (1) The plates of the capacitor are pulled apart so that the distance between the plates triples. (2) The area of the plates increase by a factor of 6. (3) The voltage of the battery decreases by a factor of 4. Determine expressions in terms of A, d, and/or V for (a) the new capacitance, (b) the new charge, and (c) the new energy density.

15)

A massless bar of length, L, is hanging from a string that is attached 1/3 of the length of the bar from the right end. A block of mass, M, is hung from the right end. The left end of the bar has an air-filled massless capacitor of plate area, A, and plate separation, d. Find an expression for the potential difference between the plates so that this system is in equilibrium. (HINT: You will

need the equation dx dU

F −= from 225.)

ANSWERS:

(a) (b)

1) a) 1.067 x 10–10 F b) 2.34 x 1011 e–

2) a) 2.95 x 10–4 F b) 5.05 x 10–4 J/m3

M

3) a) 2 x 104 V/m

b) 6.7 x 10–3 J/m3 4) 4 x 10–3 J 5) a) 2.8 x 10–3 J b) 0.467 W

6) a)   

  

− πε=

AB AB4C o

b) 5.01 x 10–11 F c) 1.125 x 105 J/m3 7) a) 1.11 x 10–4 J/m3 b) 2.14 x 10–5 C, 5.36 x 10–5 C

8) 7.86 V 9) 2.14 V 10) 4 μF 11) 9 μF 13) a) 3.85 pF b) 3.76 pF

14) a) d

A2 C o

ε=

d2 AV b) Q = oε

2

2 o

d288 V c) u = ε

15) A

Mg dV

oε =

Physics 226 Fall 2013

Problem Set #8 1) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 2) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 3) Analyze the circuit below using a QCV chart. You must

show appropriate work for full credit. 4)

An Oppo Digital Blu-Ray player [DMP-95] (Yes, I am an audiophile.) has a power cable which has a metal that allows 9 x 1019 electrons per cubic millimeter. On average, the cable passes 1 x 1022 electrons every hour. The electrons passing through the player have a drift velocity of 4.5 μm/s. (a) What current does the Oppo draw? (b) Calculate the diameter of the cable?

5) The Large Hadron Collider at CERN creates proton beams which collide together resulting in pictures like the one at the right. Some of these beams can have a radius of 1.1 mm with a current of 1.5 mA. The kinetic energy of each proton in this beam is 2.5 MeV. (a) Calculate the number density of the protons in the beam. (b) If the beam is aimed at a metal target, how many protons would strike the screen in 1 minute?

C2 = 15 μF C1 = 8 μF

20 V

C3 = 30 μF

6)

Two copper wires are soldered together. Wire #1 has a radius of 0.7 mm. Wire #2 has a radius of 1.2 mm. Copper has a number density of 8.47 x 1028 e–/m3. The drift velocity in Wire #1 is 0.72 mm/s. If you want the current to remain the same in both, what is the drift velocity in Wire #2?

7) A nichrome cable has a current of 140 A running through

it. Between two points on the cable that are 0.22 m apart, there is a potential difference of 0.036 V (a) Calculate the diameter of the cable. (b) How much heat energy does this part of the wire emit in 1 minute?

8) A “Rockstar” toaster uses a

tungsten heating element (wire). The wire has a diameter of 1.2 mm. When the toaster is turned on at 20° C, the initial current is 1.6 A. (a) What is the current density in the wire? (b) A few seconds later, the toaster heats up and the current is 1.20 A. What is the temperature of the wire? (c) If the toaster is plugged into a standard wall outlet in Kankakee, Illinois, what is the rate that energy is dissipated from the heating element?

9) Skid runs a 10 mile line of copper cable out to his shack in

the sticks so he can have electricity to play Lord of the Rings Online. At 20ºC the resistance of the cable is 12 Ω. At 50ºC the cable emits 1.5 kJ every second. (a) What is the resistance of the cable at 50ºC? (b) What is the current running through the cable at 50ºC? (c) Calculate the current density at 50ºC.

C1 = 18 μF

Wire #1 Wire #2 C2 = 6 μF

C3 = 4 μF

C4 = 30 μF 25 V

C1 = 5 μF C2 = 4 μF

C3 = 1 μF

C4 = 12 μF

15 V

10) A modern hair dryer uses a nichrome heating element that typically is 30-gauge wire around 40 cm in length. The gauge rating on a wire refers to its diameter. In this case, 30-gauge wire has a diameter of 0.254 mm. Nichrome has a number density of 7.94 x 1028 e–/m3. If the drift velocity of the electrons in the wire is 18.7 mm/s, what is the voltage that the hair dryer is plugged into?

11) Before LCD, LED, Plasma,

and (the latest) OLED TVs, there were CRT (Cathod-Ray Tube) TVs. Inside these TVs were electron guns that shot an electron beam of diameter 0.5 mm and current density of 244 A/m2 onto the inside of a glass screen which was coated with phosphor. How many electrons would hit the phosphor every minute?

12)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

13)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

14)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

15) Design a circuit that has an equivalent resistance of

1.00 Ω using at least one of each of the following resistors: a 1 Ω, a 2 Ω, and a 6 Ω. [You must also show where your A and B terminals are located.]

ANSWERS:

NOTE: Some of these answers are minimal since there are checks that you can do to verify your answers.

A

27 Ω

B 54 Ω

8 Ω

30 Ω

16 Ω

14 Ω

10 Ω

30 Ω

B

18 Ω

96 Ω

6 Ω

32 Ω 18 Ω

60 ΩA

A

20 Ω

30 Ω

B

30 Ω

7 Ω

50 Ω

12 Ω

45 Ω

60 Ω

1) CEQ = 18 μF 8) a) 1.415 x 106 A/m2

2) CEQ = 6 μF b) 94.1ºC 3) CEQ = 2 μF c) 144 W

9) a) 13.4 Ω 4) a) 0.444 A b) 2.96 mm b) 10.58 A

c) 5.14 x 105 A/m2 5) a) 1.13 x 1014 p+/m3 b) 5.63 x 1017 p+ 10) 95.0 V 6) 0.262 mm/s 11) 1.8 x 1016 e–

7) a) 0.033 m 12) 4 Ω b) 302 J 13) 14 Ω 14) 22 Ω

Physics 226 Fall 2013

Problem Set #9

NOTE: You can only use circuit tricks on 9 – 11 but not on any others. 1) Analyze the following circuit using a VIR chart. 2) Swap the location of the battery and R1 in the circuit from

problem #1. Analyze the circuit using a VIR chart. 3) Analyze the following circuit using a VIR chart. 4) The battery in this problem has an internal resistance of

0.15 Ω. (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

5) Analyze the following circuit using a VIR chart.

6) Analyze the following circuit using a VIR chart. 7) The battery in this problem has an internal resistance of

1 Ω. (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

8) A load of 3.5 Ω is connected across a 12 V battery. You

measure a voltage of 9.5 V across the terminals of the battery. (a) Find the internal resistance of the battery. (b) Is this circuit well designed? Discuss, explain.

9) Analyze the circuit from problem

#5 using a VIR chart. You are using only the diagram in #5, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

10) Analyze the circuit from problem

#6 using a VIR chart. You are using only the diagram in #6, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

R1

20 V

R2 R3 R4

R5

Given: R1 = 12 Ω R2 = 3 Ω R3 = 8 Ω R4 = 36 Ω R5 = 15 Ω

50 V

R1 Given: R1 = 28 Ω R2 = 6 Ω R3 = 84 Ω R4 = 7 Ω R5 = 54 Ω

R3

R2

R4

R5

55 V

R1 Given: R1 = 18 Ω R2 = 32 Ω R3 = 15 Ω R4 = 21 Ω R5 = 42 Ω R6 = 30 Ω R7 = 52 Ω

R3

R2

R4 R5

R6 R7

R1

VB

R2

R3 R4

Given: VB = 60 V V2 = 50 V

I1 = 2 A I4 = 3 A

R3 = 8 Ω

R1

VB

R2 R3

R4

R5

Given: V5 = 32 V

I2 = 0.4 A I4 = 0.5 A

R1 = 36 Ω R6 R3 = 60 Ω R4 = 36 Ω R6 = 32 Ω

Given: R1

VB

VB = 32 V V2 = 16 V R2 R3

I1 = 4 A

R3 = 12 Ω R4 R4 = 8 Ω

Given: VB = 63 V R1 = 8 Ω R2 = 20 Ω R3 = 35 Ω R4 = 49 Ω

Given: VB = 75 V R1 = 16 Ω R2 = 40 Ω R3 = 48 Ω R4 = 24 Ω R5 = 8 Ω R6 = 24 Ω

11) Analyze the following circuit using a VIR chart. 12) Using the information you are

given for the circuit at the right, answer the following. (a) Determine the magnitude and direction of the current in the circuit. (b) Determine which point, A or B, is at a higher potential.

13) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

14) Calculate the unknown currents I1, I2, and I3 for the circuit below.

Given: 15) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

ANSWERS:

NOTE: These answers are minimal since there are checks that you can do to verify your answers.

R1

R3 R4

R5 R6

I1 8 VVB = 50 V

R1 = 9 Ω R2 = 4 Ω R3 = 18 Ω R4 = 4 Ω R5 = 7 Ω R6 = 12 Ω

B

A

17 V

13 Ω 7 Ω

5 Ω

11 Ω

23 V

6 Ω

1 Ω

10 V

25 V

3 Ω

5 Ω

7 Ω

I1

I2

I3

4 Ω

9 Ω

10 Ω

4 Ω 7 Ω

I2

6 Ω

I3 22 V

3 Ω 10 VI1

4 Ω

4 Ω 25 V

2 Ω 5 Ω

I2 I3

20 V4 Ω

7) REQ = 8 Ω 1) REQ = 2 Ω 8) a) 0.923 Ω 2) REQ = 11.48 Ω 9) REQ = 21 Ω 3) REQ = 25 Ω 10) REQ = 25 Ω 4) REQ = 12.15 Ω 11) REQ = 20 Ω 5) REQ = 12 Ω 12) a) 1.11 A 6) REQ = 40 Ω

Physics 226 Fall 2013

Problem Set #10 1) Given the circuit at the right in

which the following values are used: R1 = 6 MΩ, R2 = 12 MΩ, and C = 3 μF. (a) You close the switch at t = 0. Find all voltages and currents for the resistors. (b) After a long time find all voltages and currents for the resistors. (c) At t = 20 s find the voltage across the capacitor. (d) Find the time constant of the capacitor. (e) Find the half- life of the circuit.

2) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

3) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

4) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors. 24 V

5) Given the circuit at below, do the following. (a) Find all voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

6) You have a current, I, flowing

through a loop of blue wire of radius, R. (a) Using the current version of the Biot- Savart Law (the cross product form), derive an equation for the total magnetic field at the center of the loop. (b) In what direction does the field point?

R1

R2

C

R1

R2 R3

R4

R5

C1

C2

VB

Given:

VB = 35 V R3 = 5 Ω R4 = 8 Ω R1 = 30 Ω R5 = 12 Ω R2 = 15 Ω

R1

R2 R3

R4

C1

C2 VB

R1 R2 Given:

Given:

VB = 60 V R1 = 4 Ω R2 = 6 Ω R3 = 12 Ω R4 = 8 Ω

VB = 50 V VB R4

R3 R1 = 60 Ω C2 R2 = 45 Ω

R3 = 90 Ω R4 = 15 Ω

C1

Given:

VB = 36 V

R1 = 10 Ω R2 = 4 Ω R3 = 40 Ω R4 = 4 Ω

R1

C1 R3 R2

R4 VB

C2

y I

z x

7) You have an arc-ed “loop” of wire that has 6 A of current flowing in the direction shown. The inner arc has a radius of 5 cm and the outer arc has a radius of 8 cm. Adapting the work you did from Problem #6, calculate the magnitude and direction of the total magnetic field at point P.

8) You have two current carrying wires #1 and #2 that are

perpendicular to the page with currents running in opposite directions as shown. Wire #1 has 5 A of current and Wire #2 has 8 A of current. (a) Find the magnitude and direction of the total B-field at point A. (b) Find the magnitude of the total B-field at point B.

9) Use the same physical situation as in Problem #8 with the

exception that both currents are pointing out of the page. (a) Find the magnitude and direction of the total B-field at point A. (b) Find the magnitude of the total B-field at point B.

10) A proton moves at a speed of 2.0 x 104 m/s in a circular

path of diameter 2 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the proton’s path. (a) Calculate the strength of the magnetic field inside the solenoid. (b) What is current in the solenoid if it has 3500 turns of wire over a length of 15 cm.

11) A charged particle is

introduced into a uniform B-field of 0.3 T with an initial velocity of 3000 m/s as shown in the diagram. The charge-to-mass ratio is – 8 x 104 C/kg. (a) In what direction will the particle be deflected? Also draw a diagram of the path of the particle. (b) What is the magnitude of the acceleration of the particle? (c) Calculate the period of the path of the particle.

12) 2.5 cm B

M

S P 1.5 mm

I A metal strip of dimensions 2.5 cm by 1.5 mm is in a uniform B-field of 3 T. It has a current of 10 A flowing to the right. See diagram. A Hall voltage between points M & S is measured to be 6 μV (a) Calculate the drift velocity of the of the electrons in the metal strip. (b) What is the number density of the charge carriers in the metal? (c) Which point has a higher potential, M or S? Explain how you found this.

B

6 cm 13) The flow of blood through an

artery contains charged ions. When an external B-field is applied, a Hall voltage can be created across the diameter of the artery. Blood flow can simulate a “current” of 1.5 nA (nano-Amps) in an artery of diameter 3 mm. Blood can have a number density of charge carriers of 4.5 x 1015 e–/m3. If you apply an external B-field of 18 mT then find the following. (a) Calculate the drift velocity of the blood flow. (b) Determine the maximum Hall voltage across the artery.

14) A green wire has 6 A of current running through. A blue

rectangular loop of wire has 10 A running through it. See diagram. (a) Calculate the magnitude and direction of the force on wire segment CD due to the green wire. (b) Calculate the magnitude and direction of the net force on the rectangular loop due to the green wire. For this part you also have to comment on the contributions of segments AC and BD on the net force.

15) CSUF Staff Physicist & Sauvé

Dude, Steve Marley, designs a lab experiment that consists of two vertical support poles that are fixed to a lab bench. Surrounding each support pole is a massless conducting spring, both having the same spring constant of 125 N/m and a relaxed length of 10 cm. The springs are part of a circuit that

12 cm

#2#1 × A

v × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

× × × × × × × × × × × × × × × × × × × × ×

× × × × × × ×

3 cm

12 cm

A BI2 4 cm

C D

I1

R

includes a variable resistor, R, a battery of 90 V, and a metal bar of 60 cm, 550 g, and negligible resistance. There is also a uniform magnetic field of 4 T encompassing the experiment. See diagram. (a) Determine the height of the metal bar if R = 20 Ω. (b) Determine what you would set the resistor value to be so that the springs would be at their relaxed length.

A

N

NSWERS:

OTE: These answers are minimal since there are checks that you can do to verify your answers.

16) A 0.5 m length of wire is bent

to form a single square loop. The loop has 12 A of current running through it. The loop is placed in a magnetic field of 0.12 T as shown at the right (side view of loop). What is the maximum torque that the loop can experience?

8) a) 4.33 x 10–5 T, [S]1) a) REQ = 4 MΩ b) 2.33 x 10–5 T b) REQ = 6 MΩ 9) a) 1.0 x 10–5 T, [S] c) 10.23 V b) 2.33 x 10–5 T d) 36 s 10) a) 0.0209 T e) 25 s B b) 0.713 T 2) a) REQ = 14 Ω 11) a) South – Circle b) REQ = 20 Ω b) 7.2 x 107 m/s2 3) a) REQ = 10 Ω c) 2.62 x 10–4 s b) REQ = 30 Ω F 12) a) 8.0 x 10–5 m/s 4) a) REQ = 20 Ω b) 2.08 x 1028 e–/m3 b) REQ = 36 Ω c) M is higher 5) a) REQ = 12 Ω 13) a) 0.295 m/s b) REQ = 18 Ω b) 1.59 x 10–4 V

6) a) R2 IB oμ= 14) a) 4.8 x 10–5 N, [S]

b) 2.74 x 10–5 N, [S] b) + x 15) a) 3.52 cm 7) 1.41 x 10–5 T, [IN] b) 40 Ω 16) 0.0225 N·m

Physics 226 Fall 2013

Problem Set #11 1) An infinitely long, solid, cylindrical

conductor of radius 10 cm has a current of 0.8 A. The current is uniformly spread over the cylinder’s area and is pointing into the page. (a) Calculate the magnitude and direction of the B-field at r = 13 cm directly to the south of the center of the cylinder. (b) Calculate the magnitude and direction of the B-field at r = 7 cm directly to the west of the center of the cylinder.

2) An infinitely long wire with

1.5 A of current is pointing into the page. Surrounding the wire is an infinitely long, thin, cylindrical shell of radius 12 cm with 0.6 A of current flowing out of the page. (a) Calculate the magnitude and direction of the B-field at r = 6 cm directly to the east of the wire. (b) Calculate the magnitude and direction of the B-field at r = 18 cm directly to the north of the wire.

3) An infinitely long, solid,

cylindrical conductor of radius 4 cm has a uniform current density of 400 A/m2 pointing out of the page. An infinitely long, thin, cylindrical shell of radius 11 cm is surrounding the solid. The shell has a current of 0.8 A of current flowing into the page. (a) Calculate the magnitude and direction of the B-field at r = 14 cm directly to the north of the shell. (b) Calculate the magnitude and direction of the B-field at r = 7 cm directly to the west of the solid. (c) Calculate the magnitude and direction of the B-field at r = 2 cm directly to the east of the center of the solid.

4) Use the same physical situation as in Problem #3 with the

exception that both currents are pointing into the page and the solid has a current of 1.2 A uniformly spread throughout its area. Do (a) – (c) from Problem #3.

5) A uniform magnetic field of magnitude 0.078 T passes

through a circular area of diameter 24 cm. The magnetic field lines are oriented at an angle of 25° with respect to a line that is normal to the circular area. Calculate the flux through the surface.

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Mike is flying his Cessna Citation II twin engine jet. The length of the wings from tip to tip is 15.9 m. The jet is flying horizontally at a speed of 464 mph. The earth’s magnetic field has a vertical component of magnitude 5.0 x 10–6 T. Calculate the induced EMF between the wing tips.

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7)

A straight wire is partially bent into the shape of a circle as shown above. The radius of the circle is 2.0 cm. A uniform magnetic field of magnitude 0.55 T is directed perpendicular to the plane of the circle. Each end of the wire is then pulled so that the area of the circle shrinks to zero. This is done during a time of 0.25 s. Calculate the magnitude of the average induced EMF between the ends of the wire.

8) A circular loop of wire with a radius of 20 cm is placed in a uniform magnetic field of 0.2 T. The field is perpendicular to the plane of the loop. The loop is removed from the field in 0.3 s. Calculate the average induced EMF in the loop while it is being pulled out of the field.

9) A long, straight wire has a current

running through it to the left. Above the straight wire is a loop of wire that is moved towards the straight wire. The loop then passes over the straight wire and continues downward, away from the straight wire. See diagram. Determine the direction (clockwise or counterclockwise) of the induced current in the loop as it is (a) moved towards the wire from above, (b) moved away from the wire.

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