Question

A coil of area 500 $c{m}^2$ and 2000 turns is kept normal to a magnetic field of $4\ast {10}^{-5}Wb{m}^{-2}$ It is rotated through 180 in 0.1 s. (i) Calculate the average induced emf. (ii) If the total resistance of the circuit be $20\Omega$ calculate the induced charge.

Answer 1

$A=500c{m}^2=0.05m^2$

Number of turns $=N=2000$

$\Rightarrow B=4\times {10}^{-5}T$

$\Rightarrow △t=0.1s$

$\Rightarrow \theta =0°$ to $180°$

Change in flux $={\varphi }_r-{\varphi }_i$

$\Rightarrow {\varphi }_i=NBA\cos 0°=NBA$

${\varphi }_r=NBA\cos 180°=-NBA$

$\Rightarrow △\varphi =-2NBA$

$\Rightarrow E_{av}=\frac{-△\varphi }{△t}$

$=\frac{2NBA}{△E}$

$=\frac{2\times 1000\times 0.4\times {10}^{-4}\times 0.05}{0.1}$

$=0.04v$

$\Rightarrow R=20\Omega$

Induced current $=I=\frac{v}{R}=\frac{0.04}{20}$

$=\mathrm{0.002.}$

Hence, the answer is $\mathrm{0.002.}$