Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.
Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.
AIIMS 2013, Medium
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$\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{2 \pi-\theta}{\theta} \Rightarrow \mathrm{I}_{1} \theta=\mathrm{I}_{2}(2 \pi-\theta)...........(1)$
$\mathrm{B}_{1}=\frac{\theta}{2 \pi} \cdot \frac{\mu_{0} \mathrm{I}_{1}}{2 \mathrm{R}}$ and $\mathrm{B}_{2}=\frac{2 \pi-\theta}{2 \pi} \cdot \frac{\mu_{0} \mathrm{I}_{2}}{2 \mathrm{R}}$
Using $(1),$ we get $B_{1}=B_{2}$
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