Answer
The induced emf in the small loop is $~~5.04\times 10^{-8}~V$
Work Step by Step
In part (a), we found that the magnetic field through the center of the loop is $1.26\times 10^{-4}~T$
In part (c), we found that the magnetic field through the center of the loop is $1.26\times 10^{-4}~T$ in the opposite direction.
Since the current in the large loop changes at a constant rate, then the magnetic field also changes at a constant rate.
We can find $\frac{dB}{dt}$:
$\frac{dB}{dt} = -\frac{2.52\times 10^{-4}~T}{1.00~s} = -2.52\times 10^{-4}~T/s$
We can find the induced emf:
$\mathscr{E} = -A~\frac{dB}{dt}$
$\mathscr{E} = -(2.00\times 10^{-4}~m^2)~(-2.52\times 10^{-4}~T/s)$
$\mathscr{E} = 5.04\times 10^{-8}~V$
The induced emf in the small loop is $~~5.04\times 10^{-8}~V$
