Question

A wire in the form of a circular loop of radius r lies with its plane normal to a magnetic field B. If the wire is polled to take a square shape in the same plane in time t, the emf induced in the loop is given by

• A. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{10})$
• B. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{8})$
• C. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{6})$
• D. $\frac{\pi B{r}^2}{t}(1-\frac{\pi }{4})$

Answer 1

The correct option is D

$\frac{\pi B{r}^2}{t}(1-\frac{\pi }{4})$

$Inducedemf\left(e\right)=\frac{magneticfield\times changeinarea}{time}=\frac{B\Delta A}{t}Sincethecircumferenceofthecircularloop=2\pi r,thesideofthesquareloop=\frac{2\pi r}{4}=\frac{\pi r}{2}.Therefore,\Delta A=\pi r^2-{\left(\frac{\pi r}{2}\right)}^2=\pi r^2(1-\frac{\pi }{4})\therefore e=\frac{B\left(\pi r^2\right)}{t}(1-\frac{\pi }{4})$