Exam 31: Faradays Law

A 400-turn circular coil (radius = 1.0 cm) is oriented with its plane perpendicular to a uniform magnetic field which has a magnitude that varies sinusoidally with a frequency of 90 Hz. If the maximum value of the induced emf in the coil is observed to be 4.2 V, what is the maximum value of the magnitude of the varying magnetic field?

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, the point(s) at highest potential is(are)

A 500-turn circular loop 15.0 cm in diameter is initially aligned so that its axis is parallel to the Earth's magnetic field. In 2.77 ms the coil is flipped so that its axis is perpendicular to the Earth's field. If a voltage of 0.166 V is induced in the coil, what is the value of the Earth's magnetic field?

A long solenoid (radius = 3.0 cm, 2 500 turns per meter) carries a current given by I = 0.30 sin(200 t) A, where t is measured in s. When t = 2.5 ms, what is the magnitude of the induced electric field at a point which is 4.0 cm from the axis of the solenoid?

A metal rod of length L in a region of space where a constant magnetic field points into the page rotates clockwise about an axis through its center at constant angular velocity ω. While it rotates, the point(s) at lowest potential is(are)

As shown below, a square loop of wire of side a moves through a uniform magnetic field of magnitude B perpendicular to the page at constant velocity directed to the right. Judd says that the emf induced in the loop is zero. Roger claims that it has magnitude B . Which one, if either, is correct, and why?

A coil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius = 8.0 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in a time of 20 ms. What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mT?

A square loop (length along one side = 20 cm) rotates in a constant magnetic field which has a magnitude of 2.0 T. At an instant when the angle between the field and the normal to the plane of the loop is equal to 20° and increasing at the rate of 10°/s, what is the magnitude of the induced emf in the loop?

An AC generator consists of 6 turns of wire. Each turn has an area of 0.040 m². The loop rotates in a uniform field (B = 0.20 T) at a constant frequency of 50 Hz. What is the maximum induced emf?

A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is changing width so that the distance x changes at a constant rate of 4.0 cm/s, what is the magnitude of the emf induced in the loop at an instant when x = 6.0 cm? Let a = 2.0 cm, b = 1.2 m, and I = 30 A.

A square coil (length of side = 24 cm) of wire consisting of two turns is placed in a uniform magnetic field that makes an angle of 60° with the plane of the coil. If the magnitude of this field increases by 6.0 mT every 10 ms, what is the magnitude of the emf induced in the coil?

In a demonstration, a 4.00 cm² square coil with 10000 turns enters a larger square region with a uniform 1.50 T magnetic field at a speed of 100 m/s. The plane of the coil is perpendicular to the field lines. If the breakdown voltage of air is 4000 V/cm on that day, the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is

A rectangular coil of 100 turns measures 40.0 cm by 20.0 cm. This coil is placed next to an electromagnet which is switched on, increasing the magnetic field through the coil from zero to 0.800 T in 50.0 ms. If the resistance of the coil is 2.0 ohms, what are the induced voltage and current in the coil?

A bar (L = 80 cm) moves on two frictionless rails, as shown, in a region where the magnetic field is uniform (B = 0.30 T) and into the paper. If v = 50 cm/s and R = 60 mΩ, what is the magnetic force on the moving bar?

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,

A car with a radio antenna 1.0 m long travels at 80 km/h in a locality where the Earth's magnetic field is 5.0 × 10−⁵ T. What is the maximum possible emf induced in the antenna as a result of moving through the Earth's magnetic field?

A conducting rod (length = 80 cm) rotates at a constant angular rate of 15 revolutions per second about a pivot at one end. A uniform field (B = 60 mT) is directed perpendicularly to the plane of rotation. What is the magnitude of the emf induced between the ends of the rod?

A conducting bar of length L rotates with a constant angular speed of +2.0 rad/s about a pivot P at one end, as shown. A uniform magnetic field (magnitude = 0.20 T) is directed into the paper. If L = 0.40 m, what is the potential difference, V_A − V_P?

A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct?

A bolt of lightning strikes the ground 200 m from a 100-turn coil oriented vertically and with the plane of the coil pointing toward the lightning strike. The radius of the coil is 0.800 m and the current in the lightning bolt falls from 6.02 × 10⁶ A to zero in 10.5 μs. What is the voltage induced in the coil over this time period? [A question for future electrical engineers: is there any way to get lightning to strike repeatedly at the same point?] ​