Answer
The amplitude of the induced electric field is $~~0.15~V/m$
Work Step by Step
We can write an expression for the magnetic field:
$B = (29.8~T)+(0.20~T)~sin(2\pi ft)$
$\frac{dB}{dt} = [(0.20~T)(2\pi f)]~cos(2\pi ft)$
Note that $r = 1.6~cm$ is less than the radius of the magnet.
We can find an expression for the induced electric field:
$2\pi~r~E = -\frac{d\Phi}{dt}$
$2\pi~r~E = -A~\frac{dB}{dt}$
$2\pi~r~E = -[(\pi~r^2)(0.20~T)(2\pi f)]~cos(2\pi ft)$
$E = -[\frac{(r)(0.20~T)(2\pi f)}{2}]~cos(2\pi ft)$
We can find the amplitude of the induced electric field:
$\frac{(r)(0.20~T)(2\pi f)}{2} = \frac{(0.016~m)(0.20~T)(2\pi) (15~Hz)}{2} = 0.15~V/m$
The amplitude of the induced electric field is $~~0.15~V/m$
