Exam 24: Capacitance and Dielectrics

Lenz's law: 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

Lenz's law: 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?

Lenz's law: 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?

LR circuits: A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch. If the switch is closed at time t = 0 s, what is the current 7.0 ms later?

Induced electric fields: For a long ideal solenoid having a circular cross-section, the magnetic field strength within the solenoid is given by the equation B(t) = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid, find the radius of the solenoid.

Lenz's law: 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

LC circuits: In an LC circuit containing a 40-mH ideal inductor and a 1.2-mF capacitor, the maximum charge on the capacitor is 45 mC during the oscillations. What is the maximum current through the inductor during the oscillations?

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

LC circuits: An LC circuit consists of a 3.4-µF capacitor and a coil with a self-inductance 0.080 H and no appreciable resistance. At t = 0 the capacitor has a charge of 5.4 µC and the current in the inductor is zero. (a) How long after t = 0 will the current in the circuit be maximum? (b) What will be this maximum current?

Motional emf: The figure shows three metal coils labeled A, B, and C heading towards a region where a uniform static magnetic field exists. The coils move with the same constant velocity and all have the same resistance. Their relative sizes are indicated by the background grid. As they enter the magnetic field the coils will have an induced electric current in them. For which coil will the current be the greatest?

Induced electric fields: A capacitor is charging in a simple RC circuit with a dc battery. Which one of the following statements about this capacitor is accurate?

Lenz's law: 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

LR circuits: 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?

AC generator: Suppose that you wish to construct a simple ac generator having an output of 12 V maximum when rotated at 60 Hz. A uniform magnetic field of 0.050 T is available. If the area of the rotating coil is 100 cm², how many turns do you need?

Flux: A circular loop of radius 0.10 m is rotating in a uniform external magnetic field of 0.20 T. Find the magnetic flux through the loop due to the external field when the plane of the loop and the magnetic field vector are (a) parallel. (b) perpendicular. (c) at an angle of 30° with each other.

LR circuits: For the circuit shown in the figure, the switch has been open for a very long time. (a) What is the potential drop across the 15.0-mH inductor just after closing the switch? (b) What is the potential drop across the 70.0-µF capacitor after the switch has been closed for a very long time?

LR circuits: An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with an open switch, a 15.0-Ω resistor, and a battery of internal resistance 5.00 Ω and open-circuit terminal voltage of 25.0 V. (μ₀ = 4π × 10^-7 T ∙ m/A) (a) What is the maximum amount of energy that the solenoid will store after closing the switch? (b) How long after closing the switch will it take for the stored energy in the solenoid to reach one-half of its maximum value?

Lenz's law: The long straight wire in the figure carries a current I that is decreasing with time at a constant rate. The circular loops A, B, and C all lie in a plane containing the wire. The induced emf in each of the loops A, B, and C is such that

Transformers: A transformer changes the 10,000 V power line to 230 V. If the primary coil contains 750 turns, how many turns are on the secondary?

AC generator: 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?