A square loop of side 2 cm is placed in a time varying magnetic...

Given:
Side of the square loop, $a = 2$ cm $= 2 \times 10^{-2}$ m
Area of the loop, $A = a^2 = 4 \times 10^{-4}$ m$^2$
Magnetic field, $B = 0.4 \sin(300t)$ T
Angle between the normal to the plane and the magnetic field, $\theta = 60^\circ$

The magnetic flux through the loop is given by:
$\Phi = \vec{B} \cdot \vec{A} = B A \cos\theta$
$\Phi = (0.4 \sin(300t))(4 \times 10^{-4}) \cos(60^\circ)$
$\Phi = 1.6 \times 10^{-4} \sin(300t) \times \dfrac{1}{2}$
$\Phi = 0.8 \times 10^{-4} \sin(300t)$ Wb

By Faraday's law of induction, the induced emf is:
$e = -\dfrac{d\Phi}{dt}$
$e = -\dfrac{d}{dt} (0.8 \times 10^{-4} \sin(300t))$
$e = -0.8 \times 10^{-4} \times 300 \cos(300t)$
$e = -240 \times 10^{-4} \cos(300t)$ V
$e = -24 \times 10^{-3} \cos(300t)$ V

The maximum induced emf is the amplitude of $e$:
$e_{\text{max}} = 24 \times 10^{-3}$ V $= 24$ mV

Answer: $24$