The radius of a circular current carrying coil is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2 \sqrt{2}}$ times that at the centre?
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(c)
$\frac{\mu_0 i R^2}{2\left(R^2+x^2\right)^{3 / 2}}=\frac{1}{2 \sqrt{2}} \frac{\mu_0 i}{2 R}$
$2 \sqrt{2} R^3=\left(R^2+x^2\right)^{3 / 2}$
$(2 \sqrt{2})^{2 / 3} R^2=R^2+x^2$
$x^2=2 R^2-R^2=R^2 \Rightarrow x=R$
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