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 the 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. $2.0\times {10}^{-7}T$

Answer 1

Answer: (A)

$1.0\times {10}^{-5}T$

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