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Two concentric circular coils of 10 turns each are situated in the same plane with common centre. Their radii are 20cm and 40cm and they carry currents of 0.2A and 0.3A respectively in opposite directions. If $μ_{0}$ is the permeability of vacuum, then the magnetic field in $W b m^{- 2}$ at their common centre is

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$\frac{35 μ_{0}}{4}$

$\frac{5 μ_{0}}{4}$

$\frac{μ_{0}}{8}$

$\frac{7 μ_{0}}{8}$

answer is B.

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Detailed Solution

$B = \frac{μ_{0} N}{2} (\frac{i_{1}}{r_{1}} - \frac{i_{2}}{r_{2}})$

$\begin{array}{l} B = \frac{μ_{0} 10}{2} [\frac{0.2}{20} - \frac{0.3}{40}] 10^{2} \\ = 5 μ_{0} [1 - \frac{3}{4}] \\ = \frac{5 μ_{0}}{4} \end{array}$

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