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 $2\times {10}^{-2}T$. If the coil form a closed loop of resistance $8\Omega$, then the average power loss due to joule heating is

• A. $2.07\times {10}^{-3}W$
• B. $1.23\times {10}^{-3}W$
• C. $3.14\times {10}^{-3}W$
• D. $1.80\times {10}^{-3}W$

Answer 1

Answer: (A)

$2.07\times {10}^{-3}W$

Here, $r=6cm=6\times {10}^{-2}m$,
N= 20, $\Omega =40rad{s}^{-1}$
$B=2x{10}^{-2}T,R=8\Omega$
Maximum emf induced, $ϵ=NAB\Omega$
$=N\left(\pi r^2\right)B\Omega$
$=20\times \pi \times (6\times {10}^{-2}{)}^2\times 2\times {10}^{-2}\times 40=0.18V$
Average value of emf induced over a full cycle ${ϵ}_{av}=0$
Maximum value of current in the coil,
$I=\frac{ϵ}{R}=\frac{0.18}{8}=0.023A$
Average power dissipated,
$P=\frac{ϵI}{2}=\frac{0.18\times 0.023}{2}=2.07\times {10}^{-3}W$