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Q.

What is the magnetic field at the common centre of the wire circuit (continuous line) as shown in fig?

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a

$\frac{μ_{0} i}{8} [\frac{1}{R_{1}} + \frac{3}{R_{2}}]$

b

$\frac{μ_{0} i}{8} [\frac{3}{R_{1}} + \frac{1}{R_{2}}]$

c

$\frac{μ_{0} i}{8} [\frac{3}{R_{1}} - \frac{1}{R_{2}}]$

d

$\frac{μ_{0} i}{8} [\frac{1}{R_{1}} + \frac{1}{R_{2}}]$

answer is B.

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Detailed Solution

$\begin{array}{l} B = \frac{μ_{0}}{4 π} \frac{(3 π / 2) i}{R_{1}} + \frac{μ_{0}}{4 π} \frac{(π / 2) i}{R_{2}} \\ = \frac{μ_{0}}{4} \times \frac{i}{2} [\frac{3}{R_{1}} + \frac{1}{R_{2}}] \\ = \frac{μ_{0} i}{8} [\frac{3}{R_{1}} + \frac{1}{R_{2}}] \end{array}$

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