Concept #1: Faraday's Law

Practice: Two solenoids are placed end to end, with one solenoid connected to a variable power source, and the other solenoid connected to a 10 Ω resistor. The first solenoid has 10 turns per cm and has as an initial current of 2 A, and the second solenoid has 5 turns and a radius of 2 cm.

a) What is the change in magnetic field emitted by the first solenoid if the current increases from 2 A to 5 A in 1 s?

b) What is the change in the magnetic flux through the other solenoid during this 1 s?

c) What is the induced EMF on the second solenoid?

d) What is the induced current on the second solenoid?

Example #1: Current in a Circuit with a Changing Magnetic Field

Practice: A square conducting wire of side length 4 cm is in a 2 T magnetic field. It rotates such that the angle of the magnetic field to the normal of the square increases from 30° to 60° in 2 s. What is the induced current on the wire if its resistance is 5 mΩ?

A constant magnetic field of 0.70 T is applied to a rectangular loop of area 3.4×10 -3 m2. If the area of this loop changes from its original value to a new value of 1.6×10 -3 m2 in 1.6 s, what is the emf induced in the loop?
A) 0 V
B) 7.9 x 10 -4 V
C) 1.6 x 10 -2 V
D) 7.5 x 10 -2 V

A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0o with a magnetic field of 1.10 T to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf induced in the coil?

A small circular loop of wire of radius 0.05 m and reisstance 1.0x10 -3 Ω is centered inside a large circular loop of wire of radius 0.5 m. The larger loop, which initially carries a current of 8.0 A, is cut and its current is reduced to zero over a time inteval of 1.0x10-6 s. Find the average current in the smaller loop during this time interval. (The magnetic field of the larger loop is approximately constant over the smaller loop).

A closed loop conductor with radius 2.0 m is located in a changing magnetic field. If the maximum emf induced in the loop is 7.0 V, what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loops lies?
A) 7.0 T/s
B) 0.080 T/s
C) 3.5 T/s
D) 0.56 T/s

A coil with 50 turns and a radius of 7 cm is placed in a 5 mT external magnetic field, ortiented such that the field is directed straight through the coil. The coil begins to rotate, while simultaneously the magnetic field strength begins to decrease. If the coil rotates until its normal is at a 60° angle from the magnetic field in 2s, and the magnetic field strength drops to 10 mT in the same 2s, what is the average emf induced in the coil during this process?

A long, straight wire is running through the center of a coil of wire, with the normal of the coil aligned along the length of the wire. The coil has 50 turns, a radius of 5 cm, and a resistance of 10 Ω. During a 0.05 s interval, the current in the long wire increases from 2 A to 5 A. What is the induced current in the coil of wire?

A 75-turn conducting coil has an area of 8.5 x 10 -3 m2 and the normal to the coil is parallel to a magnetic field B. The coil has a resistance of 14Ω, At what rate (in T/s) must the magnitude of B change for an induced current of 7.0 mA to exist in the coil.

While a magnet is moved toward the end of a solenoid (as shown in the Figure below), a voltage difference is induced between the two ends of the solenoid wire. The voltage difference would be larger if
A) the speed of the magnet were increased.
B) The bar magnet produced a stronger magnetic field.
C) the solenoid contained more loops (while having the same length ).
D) All of the above statements are true.
E) Only two of the above statements are true.

If the rate of change of the magnetic field applied to a loop of wire is doubled, what happens to the induced emf in that loop assuming all the other parameters remain unchanged?
A) It is reduced by a factor of 2.
B) It is reduced by a factor of 4.
C) It stays the same.
D) It is quadrupled.
E) It is doubled.

A single piece of wire is bent into the shape of Texas, with a total area of 7.29 cm 2. This Texas shaped loop is perpendicular to a magnetic field which increases uniformly in magnitude from 0.48 T to 1.94 T in a time of 2 s. The wire has a total resistance of 2Ω. What is the current?1. 0.8201052. 0.402843. 0.2660854. 2.292185. 0.6222546. 0.5137127. 0.3525798. 0.9095349. 0.27874510. 0.5329

A flat square coil of wire with 15 turns and an area of 0.40 m 2 is placed with the plane of its area parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular to the magnetic field in a time of 0.050 s. What is the magnitude of the average induced emf in the coil?A) 6.0 VB) 36 VC) 45 VD) 90 V

A loop of wire is placed inside a large solenoid so that the plane of the loop is perpendicular to the axis of the solenoid. To be clear, the loop is oriented in the same way the coils of the solenoid are oriented. Current can be made to flow through the loop of wire if
A) the loop of wire is rotating within the solenoid, and a constant current is flowing through the solenoid wire.
B) the current flowing through the solenoid is decreasing with time.
C) a constant current is flowing through the solenoid wire.
D) All of the above statements are true.
E) Only two of the above statements are true.

Consider a coil composed of ten loops of wire. Each loop has an area of 0.23. The coil has a very large resistance and is placed in a 0.047 tesla 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 voltage induced in the coil over this time interval?
A) 0.00 V
B) 1.0 V
C) 0.0032 V
D) 0.32 V
E) 0.032 V