Question

A 100 turns coil of area of cross-section $200c{m}^2$ having $2\Omega$ resistance is held perpendicular to a magnetic field of $0.1T$. If it is removed from the magnetic field in one second, the induced charge produced in it is

• A. 0.2 C
• B. 2 C
• C. 0.1 C
• D. 1 C
• E. 20 C

Answer 1

The correct option is C 0.1 C

Since magnitude of induced emf is given by

$E_{induced}=N\frac{d\varphi }{dt}$

$E_{induced}=N\frac{d(B.A)}{dt}$

$E_{induced}=\frac{NBA}{t}$ (for finite time interval)

$i_{induced}R=\frac{NBA}{t}$

$i_{induced}tR=NBA$

$q_{induced}=\frac{NBA}{R}$ ( since q = it)

$q_{induced}=\frac{100\times 0.1\times 200\times {10}^{-4}}{2}C$

$q_{induced}=0.1C$