Two concentric coils of 10 turns each are placed in the same plane. Their radii are 20 cm and 40 cm and carry 0.2 and 0.3 amp current respec-tively in opposite directions. The magnetic induction (in Tesla) at the centre is

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$\frac{2}{3} μ_{0}$

$\frac{3}{4} μ_{0}$

$\frac{4}{5} μ_{0}$

$\frac{5}{4} μ_{0}$

answer is B.

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Detailed Solution

$\begin{array}{l} B = B_{1} - B_{2} \Rightarrow B = \frac{μ_{0} {ni}_{1}}{2 r_{1}} - \frac{μ_{0} {ni}_{2}}{2 r_{2}} \\ ∴ B = \frac{μ_{0} n}{2} (\frac{i_{1}}{r_{1}} - \frac{i_{2}}{r_{2}}) \Rightarrow B = \frac{μ_{0} \times 10}{2 \times 10^{- 2}} (\frac{0 .2}{20} - \frac{0 .3}{40}) \\ ∴ B = \frac{5 μ_{0}}{4} \end{array}$

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