Question
A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $B = 0.4sin(300t)$ Tesla. The normal to the plane of loop makes an angle of $60^{\circ}$ with the field. The maximum induced emf produced in the loop is
$\_\_\_\_$ mV.
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Solution
Sol. [Key Concept: Induced emf $= \frac{d\varphi}{dt}$ with $\varphi = BAcos\theta$; the maximum is $B_{0}A\omega cos\theta$.]
$${B = 0.4sin300t\ \theta = 60^{\circ} }{A = (0.02)^{2} = 4 \times 10^{- 4}{\text{ }m}^{2} }{\phi = BAcos\theta }{\phi = 0.4sin(300t)Acos\theta }{emf = \frac{d\phi}{dt} = 0.4\text{ }Acos\theta cos(300t) \times 300 }{\max\text{ }emf = 0.4 \times 4 \times 10^{- 4} \times 300 \times \frac{1}{2}}$$
$$\begin{matrix} & \ = 240 \times 10^{- 4}\text{ }V \\ & \ = 24mV \end{matrix}$$
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