Physics II Exam 2 160 points Name Discussion day/time

Part I. Questions 1-10. 6 points each. Multiple choice: For full credit, circle only the correct answer. For half credit, circle the correct answer and one incorrect answer.

1. Four long parallel wires each with current I (coming out of the page) are symmetrically arranged as shown. The force on wire A is directed a. to the leftb. to the rightc. upd. downe. none of these

2. The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal toA) 4Q.B) 2Q.C) Q.D) Q/2.E) Q/4.

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3) An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When the capacitor plates carry charges +Q and -Q, the capacitor stores energy U0. If the separation between the plates is doubled, how much electrical energy is stored in the capacitor?A) 4U0B) 2U0C) U0D) U0/2E) U0/4

4) Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively,

A) 1 is neutral, 2 is negative, and 3 is positive.B) 1 is neutral, 2 is positive, and 3 is negative.C) 1 is positive, 2 is neutral, and 3 is negative.D) 1 is positive, 2 is negative, and 3 is neutral.E) 1 is negative, 2 is neutral, and 3 is positive.

5) An electron traveling toward the north with speed 4.0 × 105 m/s enters a region where the Earth's magnetic field has the magnitude 5.0 × 10-5 T and is directed downward at 45° below horizontal. What is the magnitude of the force that the Earth's magnetic field exerts on the electron? (e = 1.60 × 10-19 C)A) 2.3 × 10-18 NB) 3.2 × 10-18 NC) 2.3 × 10-19 ND) 3.2 × 10-19 NE) 2.3 × 10-20 N

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6. A long wire carries an electric current into the page. What is the direction of the magnetic field due to the current, north of the wire?

NA. northB. eastC. westD. southE. out of the pageF. into the page

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7) A very long, hollow, thin-walled conducting cylindrical shell (like a pipe) of radius R carries a current along its length uniformly distributed throughout the thin shell. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

a.

b.

A) 1B) 2C) 3D) 4E) 5

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8) A circular metal ring is situated above a long straight wire, as shown in the figure. The straight wire has a current flowing to the right, and the current is increasing in time at a constant rate. Which statement is true?

c.A) There is an induced current in the metal ring, flowing in a clockwise direction.B) There is an induced current in the metal ring, flowing in a counter-clockwise direction.C) There is no induced current in the metal ring because the current in the wire is changing at a constant rate.

9. An airplane is in level flight over Antarctica, where the magnetic field of the earth is mostly directed upward, away from the ground. As viewed by a passenger facing toward the front of the plane, which wingtip is at a higher potential?a. the left wingtipb. the right wingtipc. both wingtips would be at the same potentiald. It depends on which direction the airplane is flying.e. None of these is correct.

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10. Two separate circuits wrap around a metal bar. Just after the switch is closed, how do the currents I1 and I2 flow through the resistors R1 and R2?

a. I1 flows to the left, I2 flows to the left

b. I1 flows to the left, I2 flows to the right

c. I1 flows to the left, I2 is zero

d. I1 flows to the right, I2 flows to the left

e. I1 flows to the right, I2 flows to the right

f. I1 flows to the right, I2 is zero

g. I1 is zero, I2 is zero

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Part II. Short answer/sketch. Answer questions 11-14 as completely as possible. Show your work to earn partial credit!

11. (25 points)

i y

Two long straight wires carry equal but opposite currents along the z-axis (perpendicular to the page) as shown.a) At what point on the y-axis is the total magnetic field B produced by the wires largest? What is its value Bmax there, expressed in terms of io, d, and anything else you need? What is the direction of B at this point? (Answer below.)

y where B is maximum=____________ direction of B there:_______________ Bmax=___________________________

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oi-o

b) A conducting wire loop with its axis along the y-axis is lowered at constant speed down the y-axis, as shown. Sketch the current I

induced in the loop as a function of time, for -∞<t<+∞. Assume that the loop crosses y=0 at t=0, and that a positive current corresponds to

counterclockwise current flow as viewed from above the loop. (just sketch the shape; you don't need to label particular values.)

Place sketch to the upper left here

c) Does the loop feel a force as it moves toward the wires from above?

d) If you answered "yes" to d), how is this force produced, and what is its direction? If you answered "no" to d), explain why the loop feels no force.

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12) (25 points) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from points A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.75 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. What are the magnitude and direction of the force acting on

(a) section AB of this wire?(b) section BC of this wire?(c) section CD of this wire?(d) section DE of this wire?(e) the entire wire?Answer: (a) 0.11 N perpendicular out of the page(b) 0.00 N

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13. (25 points)A magnetic balance is used to weigh objects. The mass m to be measured is hung from the center of the bar of length L suspended in a uniform magnetic field B directed into the page. The battery voltage ε can be adjusted to vary the current in the circuit. The horizontal bar is made of extremely lightweight conducting material, and is connected to the battery by thin elastic conducting wire.

a) To measure the mass, an upward force must balance the downward force due to gravity. What is this upward force? You can either use words or an equation for your answer.

b) Which point, a or b, should be the positive terminal of the battery?

c) If the maximum terminal voltage of the battery is εmax, what is the greatest mass mmax that this instrument can

measure?

d) Now suppose a long wire with current I2 is placed at a fixed distance h directly below the magnetic balance.

How does this additional current affect the net magnetic field at the location of the bar? (i.e., stronger, weaker, same, same but different direction)

e) Derive an expression for the new maximum mass that can be measured in this situation.

14. (25 points)

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L

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A long metal bar is pulled to the right at a steady speed perpendicular to a uniform magnetic field. The bar rides on parallel metal rails connected through a resistor, so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails.

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a) Calculate the magnitude of the emf induced in the circuit (in terms of the variables given in the figure below).

b) What is the direction of the current induced in the circuit?

c) Compute the current through the resistor using the variables given in the figure.

d) repeat c calculating with values for following variables: (R of bar = 1.70 ohms, bar length =3.50 m, bar speed = 5.0m/s, B = 0.750 T).

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