Two concentric circular coils of ten turns each are situated in the same plane. Their radii are $20$ and $40\, cm$ and they carry respectively $0.2$ and $0.3$ $ampere$ current in opposite direction. The magnetic field in $weber/{m^2}$ at the centre is
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(d) Two coils carrying current in opposite direction, hence net magnetic field at centre will be difference of the two fields.
i.e. ${B_{net}} = \frac{{{\mu _0}}}{{4\pi }} \cdot 2\pi N\left[ {\frac{{N{i_1}}}{{{r_1}}} - \frac{{{i_2}}}{{{r_2}}}} \right]$$ = \frac{{10{\mu _0}}}{2}\left[ {\frac{{0.2}}{{0.2}} - \frac{{0.3}}{{0.4}}} \right] = \frac{5}{4}{\mu _0}$
i.e. ${B_{net}} = \frac{{{\mu _0}}}{{4\pi }} \cdot 2\pi N\left[ {\frac{{N{i_1}}}{{{r_1}}} - \frac{{{i_2}}}{{{r_2}}}} \right]$$ = \frac{{10{\mu _0}}}{2}\left[ {\frac{{0.2}}{{0.2}} - \frac{{0.3}}{{0.4}}} \right] = \frac{5}{4}{\mu _0}$
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