Question
A conducting loop of finite resistance lies on the $x - y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A = A_{0}(1 + sint)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is:
Options
Solution
Sol. [Key Concept: Electromagnetic induction — induced emf/current]
$A = A_{0}(1 + sint)$
$$\phi = BA = BA_{0}(1 + sint)$$
$${\ \begin{matrix} & \varepsilon = - \frac{d\phi}{dt} = - BA_{0}cost \\ & I_{\text{induced}\text{~}} = \frac{\varepsilon_{\text{ind}\text{~}}}{R} = - \frac{BA_{0}}{R}cost \end{matrix} } {Power\ = P = I^{2}R = \frac{B^{2}A_{0}^{2}\cos^{2}t}{R} } {P \propto \cos^{2}t } $$
Create a free account to view solution
View Solution Free