The figure shows a uniform magnetic field that is normal to the plane of the conducting loop of resistance R. Note: the area of the non-circular portion of the circuit is negligible compared to that of the loop.
-Suppose that the radius of the loop is 0.500 m. At what rate must B change with time if the emf induced in the loop is $\pi$ volts?
A)12.0 T/s
B)18.8 T/s
C)24.0 T/s
D)37.7 T/s
E)49.2 T/s

Question

The figure shows a uniform magnetic field that is normal to the plane of the conducting loop of resistance R. Note: the area of the non-circular portion of the circuit is negligible compared to that of the loop. 
-Suppose that the radius of the loop is 0.500 m. At what rate must B change with time if the emf induced in the loop is $\pi$ volts?
A)12.0 T/s 
B)18.8 T/s 
C)24.0 T/s 
D)37.7 T/s 
E)49.2 T/s

Quizplus · Accepted Answer

The emf induced in a loop is given by $\varepsilon = -N\frac{d\Phi_B}{dt}$, where $\varepsilon$ is the emf, $N$ is the number of turns in the loop, and $\Phi_B$ is the magnetic flux through the loop. In this case, we have $N = 1$ and $\Phi_B = BA$, where $B$ is the magnetic field strength and $A$ is the area of the loop. Therefore, we have $\varepsilon = -A\frac{dB}{dt}$. Substituting the given values, we get $\pi V = -(0.500 m)^2\frac{dB}{dt}$. Solving for $\frac{dB}{dt}$, we get $\frac{dB}{dt} = -12.0 T/s$.

The Figure Shows a Uniform Magnetic Field That Is Normal π\piπ

The Figure Shows a Uniform Magnetic Field That Is Normal $\pi$