Question

(a) Th emagnetic field in a region varies as shown in figure (38-E1). Calculate the average induced emf in a conducting loop of area $2.0\times {10}^{-3}{m}^2$ placed perpendicular to the field in each of the 10 ms intervals shown. (b) In which intervals is the emf not constant? Neglect the behaviour near the ends of 10 ms intervals.

Answer 1

${\varphi }_2=B.A=0.01\times 2\times {10}^{-3}$

$=2\times {10}^{-5}[Since{\varphi }_1=0]$

$d\varphi =2\times {10}^{-5}$

$e=\frac{-d\varphi }{dt}=\frac{-2\times {10}^{-5}}{10\times {10}^{-3}}$

$=2\times {10}^{-3}=-2mV$

${\varphi }_3=B.A=0.03\times 2\times {10}^{-3}$

$=6\times {10}^{-5}$

$d\varphi =4\times {10}^{-5}$

$e=\frac{-d\varphi }{dt}=-4mV$

${\varphi }_4=B.A=0.01\times 2\times {10}^{-3}$

$=2\times {10}^{-5}$

$d\varphi =-4\times {10}^{-5}$

$e=-\frac{d\varphi }{dt}=4mV$

${\varphi }_5=B.A.=0$

$d\varphi =-2\times {10}^{-5}$

$e=\frac{-d\varphi }{dt}=-\frac{(-2)\times \left({10}^{-5}\right)}{10\times {10}^{-3}}=2mV.$

(b)Emf is not constant in case of $\to 10-20$ ms and 20 ms -30 ms as -4 mV and 4m.