Physics

CSUF Staff Physicist & Sauvé Dude, Steve

Mahrley, 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 20 cm

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.

– 4 μC 12 μC 15) – – +

6 cm The two charges above are fixed and cannot move. Find a

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

ANSWERS:

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 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

6) – 7.87 x 104 V 7) a) 2.92 x 10-17 J b) 182.2 V c) 3644 N/C

8) a)   

   

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 15) 1.5 cm

q

Q

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 F. 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 battery to 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)

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 follow capacitors: a 1 μF, a 2 μF, and a 6 μF. [You must also show where your A and B terminals are located.]

A

20 F

4 F

4 F

6 F

12 F

B

30 F

A 12 F

18 F 6 F

20 F

B

12 F 75 F

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 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)   

  

 

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

 

b) d2 AV

Q  o

c) 2 2

o

d288 Vu  

15) A

Mg dV

o 

M

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?

C1 = 8 μF C2 = 15 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 . 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 F

Wire #1 Wire #2 C2 = 6 μF

C3 = 4 μF

C4 = 30 μF 25 V

C1 = 5 F C2 = 4 μF

15 V C3 = 1 μF

C4 = 12 μF

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  using at least one of each of the follow resistors: a 1 , a 2 , and a 6 . [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 

B 54 

8 

30 

16 

14 

10 

30 

B

18 

96 

6 

32  18 

60  A

A

20 

30 

B

30 

7 

50 

12 

45 

60 

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  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  b) 302 J 13) 14  14) 22 

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

8) A load of 3.5  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  R2 = 3  R3 = 8  R4 = 36  R5 = 15 

50 V

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

R3

R2

R4

R5

55 V

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

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 

R1

VB

R2 R3

R4

R5

Given: V5 = 32 V

I2 = 0.4 A I4 = 0.5 A

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

R1

VB

Given: VB = 32 V

R2 I1 = 4 A R3 R3 = 12 

R4 R4 = 8 

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

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

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