In a co-ordinate system a hypothetical magnetic induction exist in radially outward direction from origin which is given by $\vec{B} = B_{0} \hat{r}$ where $\hat{r}$ is a unit vector in radial direction in space away from origin . A current carrying coil of radius r and current I is placed in yz plane with centre at (a,0,0) .Find magnetic force on coil

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$\frac{π B_{0} r^{2} I}{\sqrt{a^{2} + r^{2}}}$

$\frac{4 π B_{0} r^{2} I}{\sqrt{a^{2} + r^{2}}}$

$\frac{2 π B_{0} r^{2} I}{\sqrt{a^{2} + r^{2}}}$

$\frac{8 π B_{0} r^{2} I}{\sqrt{a^{2} + r^{2}}}$

answer is C.

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Detailed Solution

$d F = \int_{0}^{2 π r} B_{0} \sin θ I d l \frac{2 π B_{0} r^{2} I}{\sqrt{a^{2} + r^{2}}}$

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