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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

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Ans: (1) 1.0 × 10–5 T

Sol:

$\vec{B}={\mu_0i\over4\pi}\theta\left[{1\over r_1}-{1\over r_2}\right]\hat{k}$

$r_1=3cm=3\times10^{-2}m$

$r_2=5cm=5\times10^{-2}m$

$\theta={\pi\over4},i=10A$

$\implies\vec{B}={4\pi\times10^{-7}\over16}\times10\left[{1\over 3\times10^{-2}}-{1\over 5\times10^{-2}}\right]\hat{k}$

$\implies\left|\vec{B}\right|={\pi\over3}\times10^{-5}T$

$\approx1\times10^{-5}T$

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