Exam 24: Capacitance and Dielectrics

LR circuits: An LR circuit contains an ideal 60-V battery, a 42-H inductor having no resistance, a 24-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. How long after closing the switch will the potential difference across the inductor be 24 V?

Faraday's law: A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e^-20t T. What is the magnitude of the current induced in the coil at the time t = 2.0 s?

Energy density: How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A)

Faraday's law: As shown in the figure, a wire and a 10-Ω resistor are used to form a circuit in the shape of a square, 20 cm by 20 cm. A uniform but nonsteady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is decreased from 1.50 T to 0.50 T in a time interval of 63 ms. The average induced current and its direction through the resistor, in this time interval, are closest to

AC generator: 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?

Faraday's law: A 200-loop coil of cross sectional area 8.5 cm² lies in the plane of the page. An external magnetic field of 0.060 T is directed out of the plane of the page. The external field decreases to 0.020 T in 12 milliseconds. (a) What is the magnitude of the change in the external magnetic flux enclosed by the coil? (b) What is the magnitude of the average voltage induced in the coil as the external flux is changing? (c) If the coil has a resistance of 4.0 ohms, what is the magnitude of the average current in the coil?

Faraday's law: A ten-loop coil having an area of 0.23 m² and a very large resistance is in a 0.047-T uniform magnetic field oriented so that the maximum flux goes through the coil. The coil is then rotated so that the flux through it goes to zero in 0.34 s. What is the magnitude of the average emf induced in the coil during the 0.34 s?

Lenz's law: 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

Faraday's law: A loop of radius r = 3.0 cm is placed parallel to the xy-plane in a uniform magnetic = 0.75 T . The resistance of the loop is 18 Ω. Starting at t = 0, the magnitude of the field decreases uniformly to zero in 0.15 seconds. What is the magnitude of the electric current produced in the loop during that time?

Faraday's law: The three loops of wire shown in the figure are all subject to the same uniform magnetic field that does not vary with time. Loop 1 oscillates back and forth as the bob in a pendulum, loop 2 rotates about a vertical axis, and loop 3 oscillates up and down at the end of a spring. Which loop, or loops, will have an emf induced in them?

Motional emf: A 50-cm wire placed in an east-west direction is moved horizontally to the north with a speed of 2.0 m/s. The horizontal component of the earth's magnetic field at that location is 25 μT toward the north and the vertical component is 50μT downward. What is the emf induced between the ends of the wire?

Flux: A 2.0-m long conducting wire is formed into a square and placed in the horizontal A uniform magnetic field is oriented above the horizontal with a strength of What is the magnetic flux through the square?

Lenz's law: In the figure, a straight wire carries a steady current I perpendicular to the plane of the page. A bar is in contact with a pair of circular rails, and rotates about the straight wire. The direction of the induced current through the resistor R is

Energy in an inductor: A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it. What is the winding density of the solenoid? (μ₀ = 4π × 10^-7 T ∙ m/A)

Transformers: When a current of 2.0 A flows in the 100-turn primary of an ideal transformer, this causes 14 A to flow in the secondary. How many turns are in the secondary?

Self-inductance: In the figure, the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of 9.6 A/s. The self-induced emf in the solenoid is found to be 8.4 V. (a) What is the self-inductance of the solenoid? (b) Which point, a or b is at higher potential?

LR circuits: 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?

Lenz's law: A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the direction of the induced current in this coil as the field fades?

LR circuits: What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of ?

Lenz's law: A circular loop of wire lies in the plane of the paper. An increasing magnetic field points out of the paper. What is the direction of the induced current in the loop?