Question

A coil has $200$ turns and area of $70 \, cm^{2}$ . The magnetic field perpendicular to the plane of the coil is $0.3 \, Wb \, m^{- 2}$ and takes $0.1 \, s$ to rotate through $180^\circ $ . The value of the induced E.M.F. will be

• A. $8.4 \, V$
• B. $84 \, V$
• C. $42 \, V$
• D. $4.2 \, V$

Answer 1

Answer: (A)

Induced $EMF$ is,
$E=-N\frac{\Delta \phi}{\Delta t}$
$E=\frac{- N B A \left(cos \left(\theta \right)_{2} - cos ⁡ \left(\theta \right)_{1}\right)}{\Delta t}$
$E=-\frac{N B A \left(cos 1 \left(80\right)^{o} - \left(cos\right)^{o} ⁡ 0\right)}{\Delta t}$
$E=\frac{2 N B A}{t}$
$E=\frac{2 \left(200\right) \left(0.3\right) \left(70 \times 1 0^{- 4}\right)}{0.1}$
$E=8.4 \, V$