Exam 31: Faradays Law

A rod (length = 10 cm) moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12-Ω load resistor?

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates about an axis through its center at constant angular velocity ω. The ends, A and E, make contact with a split ring that connects to an external circuit. The current in the external circuit of resistance R has magnitude

Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?

A planar loop consisting of four turns of wire, each of which encloses 200 cm², is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0 Ω?

A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200πt) A, where t is measured in s. When t = 5.0 ms, what is the magnitude of the induced electric field at a point which is 2.0 cm from the axis of the solenoid?

A rectangular loop (area = 0.15 m²) turns in a uniform magnetic field with B = 0.20 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is (π/2) rad and increasing at the rate of 0.60 rad/s, what is the magnitude of the emf induced in the loop?

A 5-turn square loop (10 cm along a side, resistance = 4.0 Ω) is placed in a magnetic field that makes an angle of 30° with the plane of the loop. The magnitude of this field varies with time according to B = 0.50t², where t is measured in s and B in T. What is the induced current in the coil at t = 4.0 s?

A long solenoid has a radius of 4.0 cm and has 800 turns/m. If the current in the solenoid is increasing at the rate of 3.0 A/s, what is the magnitude of the induced electric field at a point 2.2 cm from the axis of the solenoid?

An electric field of 4.0 μV/m is induced at a point 2.0 cm from the axis of a long solenoid (radius = 3.0 cm, 800 turns/m). At what rate is the current in the solenoid changing at this instant?

A long solenoid has a radius of 2.0 cm and has 700 turns/m. If the current in the solenoid is decreasing at the rate of 8.0 A/s, what is the magnitude of the induced electric field at a point 2.5 cm from the axis of the solenoid?

In the arrangement shown, a conducting bar of negligible resistance slides along horizontal, parallel, frictionless conducting rails connected as shown to a 2.0-Ω resistor. A uniform 1.5-T magnetic field is perpendicular to the plane of the paper. If L = 60 cm, at what rate is thermal energy being generated in the resistor at the instant the speed of the bar is equal to 4.2 m/s?

A 20-cm length of wire is held along an east-west direction and moved horizontally to the north with a speed of 3.0 m/s in a region where the magnetic field of the earth is 60 μT directed 30° below the horizontal. What is the magnitude of the potential difference between the ends of the wire?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is closed,

At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm² be rotated in a uniform 30-mT magnetic field to have a maximum value of the induced emf equal to 8.0 V?

A conducting rod (length = 2.0 m) spins at a constant rate of 2.0 revolutions per second about an axis that is perpendicular to the rod and through its center. A uniform magnetic field (magnitude = 8.0 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the potential difference between the center of the rod and either of its ends?

A 50-turn circular coil (radius = 15 cm) with a total resistance of 4.0 Ω is placed in a uniform magnetic field directed perpendicularly to the plane of the coil. The magnitude of this field varies with time according to B = A sin (αt), where A = 80 μT and α = 50π rad/s. What is the magnitude of the current induced in the coil at t = 20 ms?

A conducting bar moves as shown near a long wire carrying a constant 50-A current. If a = 4.0 mm, L = 50 cm, and v = 12 m/s, what is the potential difference, V_A − V_B?

Starting outside the region with the magnetic field, a single square coil of wire enters, moves across, and then leaves the region with a uniform magnetic field perpendicular to the page so that the graph shown below represents the induced emf. The loop moves at constant velocity . As seen from above, a counterclockwise emf is regarded as positive. In which direction did the loop move over the plane of the page?

Two bulbs are shown in a circuit that surrounds a region of increasing magnetic field directed out of the page. When the switch is open,

A 40-turn circular coil (radius = 4.0 cm, total resistance = 0.20 Ω) is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as given by B = 50 sin(10 πt) mT where t is measured in s. What is the magnitude of the induced current in the coil at 0.10 s?