Question

A circular coil of radius 6 cm and 20 turns rotates about its vertical diameter with an angular speed of 40 rad $s^{- 1}$ in a uniform horizontal magnetic field of magnitude 2 × 10-2 T. If the coil form a closed loop of resistance 8 $\Omega$, then the average power loss due to joule heating is

• A. 2.07 x 10-3 W
• B. 1.23 x 10-3 W
• C. 3.14 x 10-3 W
• D. 1.80 x 10-3 W

Answer 1

Answer: (A)

2.07 x 10-3 W

Answer 2

Here

$r = 6cm = 6 \times 10^{- 2}m,N = 20,\omega = 40rads^{- 1}$

$B = 2 \times 10^{- 2}T,R = 8\Omega$

Maximum emf induced

$\varepsilon = NAB\omega$

$= N(\pi r^{2})B\omega$

$= 20 \times \pi \times (6 \times 10^{- 2})^{2} \times 2 \times 10^{- 2} \times 40$

$= 0.18V$

Average value of emf induced over a full cycle

$\varepsilon_{av} = 0$

Maximum value of current in the coil

$I = \frac{\varepsilon}{R} = \frac{0.18}{8} = 0.023A$

Average power dissipated,

$P = \frac{\varepsilon I}{2} = \frac{0.18 \times 0.023}{2} = 2.07 \times 10^{- 3}W$