Question

A wire 88 cm long bent into a circular loop is kept with plane of the coil perpendicular to the magnetic induction $2.5Wb/m^2$ . with in 0.5 second, the coil is changed to a square and magnetic induction is increased $0.5Wb/m^2$. Calculate the e.m.f. induced in the wire.

Answer 1

$\varphi =flux=B\times A=2.5\times 3.14\times r^2$

$\because 2\pi r=88\Rightarrow =r\frac{88}{2\pi }=14cm$

so, $\varphi =2.5\times 3.14\times 0.14\times 0.14=0.154wb$

when it is a square ; $4l=88\Rightarrow l=\frac{88}{4}=22$

${\varphi }^{\prime }=B\times A^{\prime }=3\times 0.22\times 0.22=0.1452wb$

$e.m.f=\frac{\Delta \varphi }{\Delta t}=\frac{0.154-0.1452}{0.5}=0.76\times {10}^{-2}$