A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of $0.10 \mathrm {~T} \text {. }$ The field is now increased at a steady rate, reaching a value of $0.50 \mathrm {~T}$ after 4.0 seconds. What emf is induced in the coil?
A)0.016 V
B)0.021 V
C)0.026 V
D)0.031 V
E)0.036 V

Question

Quizplus · Accepted Answer

The emf induced in the coil is given by:$$\varepsilon = -N\frac{d\Phi_B}{dt}$$where $N$ is the number of turns in the coil, $\Phi_B$ is the magnetic flux through the coil, and $t$ is time.The magnetic flux through the coil is given by:$$\Phi_B = BA$$where $B$ is the magnetic field strength and $A$ is the area of the coil.Substituting these equations into the first equation, we get:$$\varepsilon = -N\frac{d(BA)}{dt}$$$$\varepsilon = -N\left(B\frac{dA}{dt} + A\frac{dB}{dt}\right)$$Since the area of the coil is constant, we have:$$\varepsilon = -NAB\frac{dB}{dt}$$Substituting the given values, we get:$$\varepsilon = -(20)(5.0 \times 10^{-2} \mathrm{~m}^2)(0.10 \mathrm{~T})\left(\frac{0.50 \mathrm{~T} - 0.10 \mathrm{~T}}{4.0 \mathrm{~s}}\right)$$$$\varepsilon = 0.025 \mathrm{~V}$$Therefore, the correct answer is A.

A Circular Coil of 20 Turns and Radius 5 0.10 T. 0.10 \mathrm {~T} \text {. }0.10 T.

A Circular Coil of 20 Turns and Radius 5 $0.10 \mathrm {~T} \text {. }$