Question

The area of a coil is $500c{m}^2$ and the number of turns in it is $2000$. It is kept perpendicular to a magnetic field of induction $4\times {10}^{-5}Wb/m^2$. The coil is rotated through $180$ in $0.1$ second. If the resistance of the total circuit is $20\Omega$, then the value of the induced charge flowing in the circuit will be :

• A. $1\times {10}^{-4}C$
• B. $2\times {10}^{-4}C$
• C. $3\times {10}^{-4}C$
• D. $4\times {10}^{-4}C$

Answer 1

The correct option is D $4\times {10}^{-4}C$

Answer is B

Initial flux through the coil, $=BA\cos \theta$

$=BA\cos 0^o$, as the coil is perpendicular to magnetic field

$=BAWb$

Final flux after the rotation,

$f=BA\cos {180}^o$, the coil is rotated through ${180}^o$

$=-BAWb$

Therefore, estimated value of the induced emf ($E$) as per Faraday's law is,

$E=\frac{N}{t}=\frac{N(BA-(-BA\left)\right)}{t}=\frac{2NBA}{t}$ -------(i)

Further, $E=IR=\frac{QR}{t}$ -------(ii)

From (i) & (ii)

$Q=\frac{2NBA}{R}=\frac{2\times 2000\times 4\times {10}^{-5}\times 500\times {10}^{-4}}{20}=4\times {10}^{-4}C$