Question

(a) The magnetic field in a region varies as shown in figure. Calculate the average induced emf in a conducting loop of area ${10}^{-3}{m}^2$ placed perpendicular to the field in each of the $10ms$ intervals shown
(b) In which interval(s), the emf is not constant? Neglect the behaviour near the ends of $10ms$ intervals.

Answer 1

a) The flux through a surface is given as

$\varphi =B\cdot A$

Area of the loop is given so flux is given as,

$\varphi =B\cdot A$

${\varphi }_1=0$

${\varphi }_2=0.01\cdot 2\times {10}^{-3}$

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

$d\varphi =0-2\times {10}^{-5}$

So, induced emf is

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

$e=2mV$

Similarly,

${\varphi }_3=0.03\cdot 2\times {10}^{-3}$

$d\varphi =\left(6-2\right)\times {10}^{-5}$

$e=-4mV$

${\varphi }_4=0.01\cdot 2\times {10}^{-3}$

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

$e=4mV$

${\varphi }_5=0$

$d\varphi =-2mV$

$e=2mV$

b) The emf is not constant in case of $10-20ms$ and $20-30ms$ respectively.