Question

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10A$. The magnetic field at point $O$ will be close to :

• A. $1.0\times 10^{-5}T$
• B. $1.5\times 10^{-5}T$
• C. $1.0\times 10^{-7}T$
• D. $1.5\times 10^{-7}T$

Answer 1

Answer: (A)

$\vec{B}=\frac{{\mu }_{0}i}{4\pi }\theta \left[\frac{1}{r_1}-\frac{1}{r_2}\right]\hat{k}$
$r_1=3cm=3\times 10^{-2}m$
$r_2=5cm=5\times 10^{-2}m$
$\theta =\frac{\pi }{4},i=10A$
$\Rightarrow \vec{B}=\frac{4\pi \times 10^{-7}}{16}\times 10\left[\frac{1}{3\times 10^{-2}}-\frac{1}{5\times 10^{-2}}\right]\hat{k}$
$\Rightarrow \left|\vec{B}\right|=\frac{\pi }{3}\times 10^{-5}T$
$\approx 1\times 10^{-5}T$