A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :
(1) 1.0 × 10–5 T
(2) 1.5 × 10–5 T
(3) 1.0 × 10–7 T
(4) 1.0 × 10–7 T
Ans: (1) 1.0 × 10–5 T
Sol:
$\vec{B}={\mu_0i\over4\pi}\theta\left[{1\over r_1}-{1\over r_2}\right]\hat{k}$
$r_1=3cm=3\times10^{-2}m$
$r_2=5cm=5\times10^{-2}m$
$\theta={\pi\over4},i=10A$
$\implies\vec{B}={4\pi\times10^{-7}\over16}\times10\left[{1\over 3\times10^{-2}}-{1\over 5\times10^{-2}}\right]\hat{k}$
$\implies\left|\vec{B}\right|={\pi\over3}\times10^{-5}T$
$\approx1\times10^{-5}T$