Physics - EMI/AC Question with Solution | TestHub

Given: The magnetic field in the region is, $\mathrm{B}=0.025\mathrm{T}$. Radius of the loop, $\mathrm{r}=2\mathrm{cm}=2\times 10^{-2}$ Constant rate at which radius of the loop shrimks, $\frac{\mathrm{dr}}{\mathrm{dt}}=1\times 10^{-3}{\mathrm{ms}}^{-1}$ To find: The induced emf in the loop when radius is 2 cm. The magnetic flux linked with the loop is given by: $\begin{array}{rl}& \varphi =\mathrm{BA}\cos \theta \\ & =\mathrm{B}\left(\pi {\mathrm{r}}^2\right)\cos {\mathrm{O}}^{\circ }\\ & \Rightarrow \mathrm{B}\pi {\mathrm{r}}^2\end{array}$ The magnitude of induced emf is given as: $\begin{array}{rl}& |ϵ|=\frac{\mathrm{d}\varphi }{\mathrm{dt}}\\ & =\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{B}\pi {\mathrm{r}}^2\right)\\ & =\mathrm{B}\pi 2\mathrm{r}\frac{\mathrm{dr}}{\mathrm{dt}}\end{array}$ Substitute the values. $\begin{array}{rl}& |ϵ|=0.025\times \pi \times 2\times 2\times 10^{-2}\times 1\times 10^{-3}\\ & =\pi \times 10^{-6}\mathrm{V}\\ & \Rightarrow \pi \mu \mathrm{V}\end{array}$