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Exam 30: Electromagnetic Induction

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Question 31

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An LR circuit contains an ideal 60-V battery, a 51-H inductor having no resistance, a 21-Ω resistor, and a switch S, all in series. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. When the voltage across the resistor is equal to the voltage across the inductor, what is the current in the circuit?

A) 1.4 A
B) 0.57 A
C) 1.1 A
D) 0.86 A
E) 1.7 A

F) C) and E)
G) A) and E)

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Question 32

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What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 4.19 nH
B) 4.19 pH
C) 4.19 µH
D) 4.19 mH
E) 4.19 H

F) B) and E)
G) None of the above

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Question 33

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In the figure, two parallel wires carry currents of magnitude I in opposite directions. A rectangular loop is midway between the wires. The current I is decreasing with time. The induced current through the resistor R is

A series circuit consists of a 0.55-H inductor with internal resistance of 8.0 Ω connected in series with a 4.0-Ω resistor, an open switch, and an ideal 12-V battery. (a) When the switch is closed, what is the initial current through the 4.0-Ω resistor? (b) What is the current through the 4.0-Ω resistor a very long time after the switch is closed?

In the figure, a straight wire carries a current I. The wire passes through the center of a toroidal coil. If the current in the wire is quickly reduced to zero, the induced current through the resistor R is

For the circuit shown in the figure, the inductors have no appreciable resistance and the switch has been open for a very long time. (a) The instant after closing the switch, what is the current through the 60.0-Ω resistor? (b) The instant after closing the switch, what is the potential difference across the 15.0-mH inductor? (c) After the switch has been closed and left closed for a very long time, what is the potential drop across the 60.0-Ω resistor?

Consider the circuit shown in the figure. The battery has emf ε = 25 volts and negligible internal resistance. The inductance is and the resistances are R₁ = 12 Ω and R₂ = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch is closed. (a) What is the current in the resistor R₁ just after the switch is closed? (b) After leaving the switch closed for a very long time, it is opened again. Just after it is opened, what is the current in R₁?

A bar magnet is held vertically with its upper end a little bit below the center of a horizontal metal ring. The upper end of the magnet is its north pole, as shown in the figure. The bar magnet is now dropped. An observer views the ring from above its center. To this observer, how will the induced current in the ring behave as the magnet falls?

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T ∙ m/A)

In the figure, a C-shaped conductor is in a uniform magnetic field B, which is increasing. The polarity of the induced emf in terminals X and Y is

In the figure, a bar magnet moves away from the solenoid. The induced current through the resistor R is

Wire is wound on a square frame, 30 cm by 30 cm, to form a coil of 7 turns. The frame is mounted on a horizontal shaft through its center (perpendicular to the plane of the diagram) , as shown in the figure. The coil is in clockwise rotation, with a period of 0.060 s. A uniform, horizontal, magnetic field of magnitude 0.40 T is present. At a given instant, the plane of the coil forms a 60° angle with the horizontal, as shown. At that instant, what is the magnitude of the emf induced in the coil?

A closed, circular loop has a counter-clockwise current flowing through it as viewed by a person on the right, as shown in the figure. If a second closed circular loop with the same radius approaches this loop with constant velocity along a common axis as shown, in what direction will a current flow in the approaching loop as viewed by the person on the right?

A charged capacitor is connected to an ideal inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. At time t = 0 the capacitor is fully charged. At a given instant later the charge on the capacitor is measured to be 3.0 μC and the current in the circuit is equal to 75 μA. What is the maximum charge of the capacitor?

In the figure, a copper bar is in contact with a pair of parallel metal rails and is in motion with velocity ν. A uniform magnetic field is present pointing downward, as shown. The bar, the rails, and the resistor R are all in the same plane. The induced current through the resistor R is

A series LR circuit contains an emf source of having no internal resistance, a resistor, a inductor having no appreciable resistance, and a switch. If the emf across the inductor is of its maximum value after the switch is closed, what is the resistance of the resistor?

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?

In the figure, two solenoids are approaching each other with speed v as shown. The induced current through the resistor R is

You are designing a generator to have a maximum emf of 8.0 V. If the generator coil has 200 turns and a cross-sectional area of 0.030 m², what should be the frequency of the generator in a uniform magnetic field of 0.030 T?

In the figure, the inner loop carries a clockwise current I that is increasing. The resistor R is in the outer loop and both loops are in the same plane. The induced current through the resistor R is