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1.A uniform magnetic field of magnitude 1.00 T is directed perpendicular to the plane of a rectangular loop having dimensions 8.5 cm by 14 cm. Find the magnetic flux through the loop.

_____mWb

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2. Find the flux of Earth's magnetic field of magnitude 5.00 10-5 T through a square loop of area 20.0 cm2 for the following:

(a) when the field is perpendicular to the plane of the loop

_____T · m2

(b) when the field makes a 60.0° angle with the normal to the plane of the loop

_____T · m2

(c) when the field makes a 90.0° angle with the normal to the plane

_____T · m2

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3. A long, straight wire carrying a current of 1.00 A is placed along the axis of a cylinder of radius 0.500 m and a length of 5.00 m. Determine the total magnetic flux through the cylinder.

____T·m2

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4. A 410 turn solenoid of length 34.0 cm and radius 3.20 cm carries a current of 5.10 A. Find the following.

(a) the magnetic field strength inside the coil at its midpoint

_____mT

(b) the magnetic flux through a circular cross-sectional area of the solenoid at its midpoint

_____T · m2

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5.A cube of edge length = 8.0 cm is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components Bx = +3.0 T, By = +2.0 T, and Bz = +5.0 T.

(a) Calculate the flux through the shaded face of the cube.

_____T · m2

(b) What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)?

_____T · m2

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6.Three loops of wire move near a long straight wire carrying a current as in the following figure.

(a) What is the direction of the induced current, if any, in loop A?

clockwise

counterclockwise

No current is induced.

(b) What is the direction of the induced current, if any, in loop B?

clockwise

counterclockwise

No current is induced.

(c) What is the direction of the induced current, if any, in loop C?

clockwise

counterclockwise

No current is induced.

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7.A circular loop of wire of radius 12.4 cm is placed in a magnetic field directed perpendicular to the plane of the loop, as shown in the figure below. If the field decreases at the rate of 0.530 T/s in some time interval, what is the magnitude of the emf induced in the loop during this interval?

_____mV

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8.A square, single-turn wire loop = 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.00 cm, as shown in the end view of the figure below. The solenoid is 21.0 cm long and wound with 90 turns of wire.

(a) If the current in the solenoid is 4.00 A, what is the magnetic flux through the square loop?

_____T · m2

(b) If the current in the solenoid is reduced to zero in 4.00 s, what is the magnitude of the average induced emf in the square loop?

_____V

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9. Consider the arrangement shown in the figure below. Assume R = 6.00 Ω and = 1.20 m, and a uniform 2.90-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.500 A in the resistor?

_____m/s

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10. A square coil of wire of side 2.00 cm is placed in a uniform magnetic field of magnitude 1.50 T directed into the page as in the figure shown below. The coil has 32.0 turns and a resistance of 0.780 Ω. If the coil is rotated through an angle of 90.0° about the horizontal axis shown in 0.335 s, find the following.

(a) the magnitude of the average emf induced in the coil during this rotation

_____mV

(b) the average current induced in the coil during this rotation

_____mA

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11.A motor has coils with a resistance of 26 and operates from a voltage of 236 V. When the motor is operating at its maximum speed, the back emf is 150 V.

(a) Find the current in the coils when the motor is first turned on.

_____A

(b) Find the current in the coils when the motor has reached maximum speed.

_____A

(c) If the current in the motor were 5.0 A at some instant, what is the back emf at that time?

_____V

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12. A technician wraps wire around a tube of length 38 cm having a diameter of 7.8 cm. When the windings are evenly spread over the full length of the tube, the result is a solenoid containing 560 turns of wire.

(a) Find the self-inductance of this solenoid.

_____mH

(b) If the current in this solenoid increases at the rate of 3 A/s, what is the self-induced emf in the solenoid?

_____mV

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13. An electromagnet can be modeled as an inductor in series with a resistor. Consider a large electromagnet of inductance L = 12.5 H and resistance R = 6.00 Ω connected to a 18.0-V battery and switch as in the figure shown below. After the switch is closed, find the following.

(a) the maximum current carried by the electromagnet

_____A

(b) the time constant of the circuit

_____s

(c) the time it takes the current to reach 95.0% of its maximum value

_____s

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14. An RL circuit with L = 4.00 H and an RC circuit with C = 9.00 µF have the same time constant.

(a) If the two circuits have the same resistance, R, what is the value of R?

_____

(b) What is this common time constant?

_____ms

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15. A battery is connected in series with a 0.31-Ω resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.10 s, and the maximum current in the circuit is 7.9 A.

(a) Find the emf of the battery.

_____V

(b) Find the inductance of the circuit.

_____mH

(c) Find the current in the circuit after one time constant has elapsed.

_____A

(d) Find the voltage across the resistor after one time constant has elapsed.

_____V

(e) Find the voltage across the inductor after one time constant has elapsed.

_____V

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16.The Sun delivers an average power of 583.9 W/m2 to the top of Mars's atmosphere. Find the magnitudes of Bmax and Emax for the electromagnetic waves at the top of the atmosphere.

Bmax =

_____T

Emax =

_____V/m

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