13.7 Applications of Electromagnetic Induction

A coil with 50 turns and area 10 $\text{cm}^{2}$ is oriented with its plane perpendicular to a 0.75-T magnetic field. If the coil is flipped over (rotated through $180 °$) in 0.20 s, what is the average emf induced in it?

The magnetic field between the poles of a horseshoe electromagnet is uniform and has a cylindrical symmetry about an axis from the middle of the South Pole to the middle of the North Pole. The magnitude of the magnetic field changes as a rate of dB/dt due to the changing current through the electromagnet. Determine the electric field at a distance r from the center.

A 120-V, series-wound dc motor draws 0.50 A from its power source when operating at full speed, and it draws 2.0 A when it starts. The resistance of the armature coils is $10 \Omega$. (a) What is the resistance of the field coils? (b) What is the back emf of the motor when it is running at full speed? (c) The motor operates at a different speed and draws 1.0 A from the source. What is the back emf in this c…

A copper wire of length L is fashioned into a circular coil with N turns. When the magnetic field through the coil changes with time, for what value of N is the induced emf a maximum?

A circular copper disk of radius 7.5 cm rotates at 2400 rpm around the axis through its center and perpendicular to its face. The disk is in a uniform magnetic field $\overset{\rightarrow}{B}$ of strength 1.2 T that is directed along the axis. What is the potential difference between the rim and the axis of the disk?

A long solenoid with 10 turns per centimeter is placed inside a copper ring such that both objects have the same central axis. The radius of the ring is 10.0 cm, and the radius of the solenoid is 5.0 cm. (a) What is the emf induced in the ring when the current I through the solenoid is 5.0 A and changing at a rate of 100 A/s? (b) What is the emf induced in the ring when $I = 2.0 \text{A}$ and $d I / d t = 100 \text{A} / \text{s} ?$ (c) What is the ele…

A 500-turn coil with a $\text{0}.\text{250}-\text{m}^{2}$ area is spun in Earth’s $5.00 \times 10^{−5} \text{T}$ magnetic field, producing a 12.0-kV maximum emf. (a) At what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

A long solenoid of radius $a$ with $n$ turns per unit length is carrying a time-dependent current $I \left(t\right) = I_{0} \text{sin} \omega t$ where $I_{0}$ and $\omega$ are constants. The solenoid is surrounded by a wire of resistance R that has two circular loops of radius b with $b > a$. Find the magnitude and direction of current induced in the outer loops at time $t = 0$.