Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry 0.2 A and 0.3 A current, respectively, in opposite direction. The magnetic field in weber/m² at the centre is

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$\frac{μ_{0}}{80}$

$\frac{35}{4} μ_{0}$

$\frac{7}{80} μ_{0}$

$\frac{5}{4} μ_{0}$

answer is D.

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Detailed Solution

Two coils carry current in opposite direction, hence net magnetic field at centre will be difference of the two fields.

$\begin{array}{l} i . e ., B_{net} = \frac{μ_{0}}{4 π} . 2 πN [\frac{i_{1}}{r_{1}} - \frac{i_{2}}{r_{2}}] \\ = \frac{10 μ_{0}}{2} [\frac{0 .2}{0 .2} - \frac{0 .3}{0 .4}] = \frac{5}{4} μ_{0} \end{array}$

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