Problem 1
A single loop of wire with an area of 0.0900 m\(^2\) is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (a) What emf is induced in this loop? (b) If the loop has a resistance of 0.600 \(\Omega\), find the current induced in the loop.
Problem 2
In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm\(^2\) is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0 \(\times\) 10\(^{-5}\) T. (a) What is the total magnetic flux through the coil before it is rotated? After it is rotated? (b) What is the average emf induced in the coil?
Problem 4
A closely wound search coil (see Exercise 29.3) has an area of 3.20 cm\(^2\), 120 turns, and a resistance of 60.0 \(\Omega\). It is connected to a charge- measuring instrument whose resistance is 45.0 \(\Omega\). When the coil is rotated quickly from a position parallel to a uniform magnetic field to a position perpendicular to the field, the instrument indicates a charge of 3.56 \(\times\) 10\(^{-5}\) C. What is the magnitude of the field?
Problem 5
A circular loop of wire with a radius of 12.0 cm and oriented in the horizontal \(xy\)-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction, which is upward. (a) If the loop is removed from the field region in a time interval of 2.0 ms, find the average emf that will be induced in the wire loop during the extraction process. (b) If the coil is viewed looking down on it from above, is the induced current in the loop clockwise or counterclockwise?
Problem 6
A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to \(B =\) (0.0120 T/s)\(t\) + (3.00 \(\times\) 10\(^{-5}\) T/s\(^4)t^4\). The coil is connected to a 600-\(\Omega\) resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. (a) Find the magnitude of the induced emf in the coil as a function of time. (b) What is the current in the resistor at time \(t =\) 5.00 s?
Problem 9
A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. (a) Find the emf induced in the loop at the instant when 9.0 s have passed. (b) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.
Problem 10
A closely wound rectangular coil of 80 turns has dimensions of \(25.0 \mathrm{~cm}\) by \(40.0 \mathrm{~cm} .\) The plane of the coil is rotated from a position where it makes an angle of \(37.0^{\circ}\) with a magnetic field of \(1.70 \mathrm{~T}\) to a position perpendicular to the field. The rotation takes \(0.0600 \mathrm{~s}\). What is the average emf induced in the coil?
Problem 11
In a region of space, a magnetic field points in the +\(x\)-direction (toward the right). Its magnitude varies with position according to the formula \(B_x = B_0 + bx\), where \(B_0\) and \(b\) are positive constants, for \(x \geq\) 0. A flat coil of area \(A\) moves with uniform speed \(v\) from right to left with the plane of its area always perpendicular to this field. (a) What is the emf induced in this coil while it is to the right of the origin? (b) As viewed from the origin, what is the direction (clockwise or counterclockwise) of the current induced in the coil? (c) If instead the coil moved from left to right, what would be the answers to parts (a) and (b)?
Problem 12
In many magnetic resonance imaging (MRI) systems, the magnetic field is produced by a superconducting magnet that must be kept cooled below the superconducting transition temperature. If the cryogenic cooling system fails, the magnet coils may lose their superconductivity and the strength of the magnetic field will rapidly decrease, or \(quench\). The dissipation of energy as heat in the now-nonsuperconducting magnet coils can cause a rapid boil-off of the cryogenic liquid (usually liquid helium) that is used for cooling. Consider a superconducting MRI magnet for which the magnetic field decreases from 8.0 T to nearly 0 in 20 s. What is the average emf induced in a circular wedding ring of diameter 2.2 cm if the ring is at the center of the MRI magnet coils and the original magnetic field is perpendicular to the plane that is encircled by the ring?
Problem 13
The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of 1.60 cm. The coil rotates in a magnetic field of 0.0750 T. What is the angular speed of the coil if the maximum emf produced is 24.0 mV?
