Question

A closed coil consists of 500 turns on a rectangular frame of area 4.0 $c{m}^2$ and has a resistance of 50 ohms. The coil is kept with its plane perpendicular to a uniform magnetic field of 0.2 wb/$m^2$, the amount of charge flowing through the coil if it is turned over. (rotated through ${180}^0$) :-

• A. $1.6\times {10}^{-3}$ C
• B. $16\times {10}^{-3}$ C
• C. $0.16\times {10}^{-3}$ C
• D. $160\times {10}^{-3}$ C

Answer 1

Answer: (A)

$1.6\times {10}^{-3}$ C

magnetic flux through the coil $\psi =NBA=500\times 0.2\times 4\times {10}^{-4}=0.04weber$

change in magnetic flux when the coil is rotated by ${180}^0⟹△\psi =0.04-(-0.04)=0.08wb$

induced emf $E$ = $\frac{△\psi }{△t}$

induced current $I=\frac{E}{R}=\frac{△\psi }{R△t}$

induced charge $q=I\times △t=\frac{△\psi }{R△t}△t=\frac{△\psi }{R}=\frac{0.08}{50}=0.0016C=1.6\times {10}^{-3}C$