Question

A coil of area 500 $c{m}^2$ having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude $4\times {10}^{-5}$ $weber/m^2$. If it is rotated by 180 about an axis passing through one of its diameter in 0.1 sec, find the average induced emf.

• A. zero.
• B. 30 mV
• C. 40 mV
• D. 50 mV

Answer 1

The correct option is C 40 mV

0iven that :- $N=1000,B=4\times {10}^{-5}weber/m^2,A=500c{m}^2=0.05m^2$

Initial flux linked with the coil, ${\varphi }_1=1000\times 4\times {10}^{-5}\times 0.05$

$⟹{\varphi }_1=2\times {10}^{-3}weber$

After rotation of ${180}^o$, B remains same but normal vector gets reversed, hence ${\varphi }_2=-{\varphi }_1$

Average EMF=$E=\frac{-\Delta \varphi }{t}$

$⟹E=-\frac{{\varphi }_2-{\varphi }_1}{t}$

$⟹E=\frac{{\varphi }_1-{\varphi }_2}{t}$

$⟹E=\frac{2{\varphi }_1}{t}$

$⟹E=\frac{4\times {10}^{-3}}{0.1}V$

$⟹E=40mV$

Answer-(C)