Answer
(a) The axis of the coil should be aligned with the magnetic field.
(b) The amplitude of the induced EMF is $3.65\times 10^{-3}~V$
(c) The amplitude of the induced EMF is $0.025~V$
Work Step by Step
(a) To detect the electromagnetic wave with a magnetic dipole antenna, the area of the coil of the antenna should be aligned so that the magnetic field passes through it. Therefore, the axis of the coil should be aligned with the magnetic field.
(b) We can find an expression for $\frac{dB}{dt}$:
$B = B_0~cos(\omega~t)$
$\frac{dB}{dt} = -B_0~\omega~sin (\omega~t)$
We can find the amplitude of the induced $EMF$:
$EMF = -N~\frac{\Delta \Phi}{\Delta t}$
$EMF = -N~\frac{\Delta B~A}{\Delta t}$
$EMF = -N~(\frac{dB}{dt})~A$
$EMF = -N~(B_0~\omega)~A$
$EMF = -N~B_0~(2\pi~f)~\pi~r^2$
$EMF = -(50)~(1.7\times 10^{-9}~T)~(2\pi)~(870\times 10^3~Hz)~(\pi)~(0.050~m)^2$
$EMF = -3.65\times 10^{-3}~V$
The amplitude of the induced EMF is $3.65\times 10^{-3}~V$
(c) We can find the amplitude of the induced EMF in an electric dipole antenna:
$EMF = E~L = (0.50~V/m)(0.050~m) = 0.025~V$
The amplitude of the induced EMF is $0.025~V$
