# Physics

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

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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.

6) × × × × × ×

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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.

×

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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×

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I

10)

Find the direction of the induced current through the resistor in the drawing below (a) at the instant the switch is closed, (b) after the switch has been closed for several minutes, and (c) at the instant the switch is opened.

11)

A wire is bent into a semicircle of radius 11 cm and connected to a resistor of 59 Ω. The semicircle is placed in a uniform magnetic field of 18 T. The semicircle rotates according to the equation, ( ) tt ω=θ , in which the angular velocity, ω, is 15 rad/s. At t = 0.759 s find the magnitude of the following values: (a) the flux through the semicircle, (b) the induced EMF in the circuit, (c) the induced current in the circuit.

12) A uniform magnetic field varies

with time according to the equation B(t) = (2 T) + (6 T/s)t. A circular loop of wire with a diameter of 2.2 m is lying in the field so that its normal is parallel to the B-field. The loop has a resistance of 11 Ω/m. At t = 1.6 s find the magnitude of the following values: (a) the flux through the loop, (b) the induced EMF in the loop, (c) the induced current in the loop, and (d) the direction of the induced current.

13) Skid needs to design a 60 Hz AC

generator to run his V8 T.A.N.K. amplifier for his gig at RoSfest. The generator needs to contain a 350- turn coil whose diameter is 1.5 cm while its maximum EMF needs to be 120 V. What should be the magnitude of the magnetic field in which the coil rotates?

14)

In the circuit above, the inductor has 975 turns of wire, a length of 4 cm, and a core diameter of 1.5 cm. (a) Calculate the inductance of the inductor. At t = 0, (b) fill out a complete VIR chart, and (c) calculate the energy stored in the inductor. At t → ∞, (d) fill out a complete VIR chart, and (e) calculate the energy stored in the inductor.

15)

In the circuit above, the inductor has 1250 turns of wire, a length of 8 cm, and a core diameter of 3 cm. (a) Calculate the inductance of the inductor. At t = 0, (b) fill out a complete VIR chart, and (c) calculate the energy stored in the inductor. At t → ∞, (d) fill out a complete VIR chart, and (e) calculate the energy stored in the inductor.

ANSWERS:

1) a) 1.23 x 10–6 T [W] b) 1.12 x 10–6 T [N] 2) a) 5 x 10–6 T [S] b) 1 x 10–6 T [E] 3) a) 1.73 x 10–6 T [W] b) 5.75 x 10–6 T [S] c) 5.03 x 10–6 T [N] 4) a) 2.86 x 10–6 T [E] b) 3.43 x 10–6 T [N] c) 3 x 10–6 T [S] 5) 1.02 x 10–3 Wb 6) 0.0165 V 7) 0.028 V 8) 0.0838 V 11) a) 0.13 Wb b) 4.75 V c) 0.0805 A

12) a) 44.1 Wb b) 22.8 V c) 0.3 A 13) 5.15 T

14) a) 5.27 mH b) 16 Ω c) 0 d) 13 Ω e) 1.17 x 10–3 J 15) a) 17.3 mH b) 15 Ω c) 0 d) 6 Ω e) 0.216 J

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

IR

R1

R2 R3

VB

LGiven:

VB = 26 V

R1 = 7 Ω R2 = 9 Ω R3 = 18 Ω

R1

R2 R3

Given:

VB = 30 V VB

LR1 = 2 Ω R2 = 12 Ω R3 = 36 Ω R4 = 4 Ω R4

Physics 226 Fall 2013

Problem Set #12 1) A step-up transformer is designed to have an output

voltage of 2200 V (rms) when the primary is connected across a 110 V (rms) source. (a) If there are 80 turns on the primary winding, how many turns are required on the secondary? (b) If a load resistor across the secondary draws a current of 1.5 A, what is the current in the primary, assuming ideal conditions?

2) An rms voltage of 100 V is applied to a purely resistive

load of 5.0 Ω. Find (a) the maximum voltage applied, (b) the rms current supplied, and (c) the maximum current supplied.

3) A 7.5 μF capacitor is attached to an AC source. It has a

reactance of 168 Ω. What is the frequency of the AC source?

4) An inductor has a reactance of 480 Ω when attached to

an AC source of frequency 1350 Hz. What is the reactance when the frequency is 450 Hz?

5) An AC source, a 275 Ω resistor, an inductor of inductive reactance 648 Ω, and a capacitor of capacitive reactance 415 Ω are arranged to form a series RLC circuit. The current in the circuit is 0.233 A. Calculate the voltage of the AC source.

6) A series RLC circuit includes a 47 Ω resistor, a 4 mH

inductor, and a 2 μF capacitor. When the frequency is 2550 Hz, what is the power factor of the circuit?

7) An AC source produces a current of 0.04 A at a

frequency of 4.8 kHz when attached to a 232 Ω resistor and a 0.25 μF capacitor that are connected in series. Calculate (a) the voltage of the AC source and (b) the phase angle between the current and the voltage across the resistor/capacitor combination.

8) A 215 Ω resistor and a 0.2 H inductor are connected

in series with an AC source of 234 V and frequency 106 Hz. (a) What is the current in the circuit? (b) Calculate the phase angle between the current and the voltage of the AC source.

9) An RLC circuit containing a 10 Ω resistor, a 17 mH

inductor, and a 12 μF capacitor are connected in series with a 155 V RMS AC source. (a) Calculate the frequency of the AC source at which the current will be a maximum. (b) Calculate the maximum value of the RMS current.

ANSWERS: