Question

A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]

• A. 0.2 T
• B. 0.3 T
• C. 0.4 T
• D. 0.05 T

Answer 1

The Correct Option is D

$NBi \, A \sin \,
heta= \tau \hspace25mm ...(i) $
N, B, i and A are constants
$\therefore \hspace15mm sin
\theta \propto 0.3 $
$\hspace15mm cos
\theta \propto 0.4 $
$\hspace15mm tan \theta = \frac {3}{4} $
From E (i)
$\hspace15mm sin \,
heta = \frac {3}{5} $
$\hspace15mm B= \frac {\tau}{NiAsin \,
heta}$
$\hspace10mm B= \frac {0.3 \times 5}{100\times5\times2\times10^{-2}\times3}=0.05 \, T$