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Q.

Infinite number of straight wires each carrying current $I$ are equally placed as shown in the figure below. Adjacent wires have current in opposite direction. Net magnetic field at point $P$ is

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a

$\frac{μ_{0} I}{4 π} \frac{l n2}{\sqrt{3} a} k^{^}$

b

$\frac{μ_{0} I}{4 π} \frac{l n4}{\sqrt{3} a} k^{^}$

c

$\frac{μ_{0} I}{4 π} \frac{l n4}{\sqrt{3} a} (- k^{^})$

d

$z e r o$

answer is B.

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Detailed Solution

$\vec{B} = \frac{μ_{0}}{4 π} I (\sin 30 ° + \sin 30 °) [\frac{1}{a \cos 30 °} - \frac{1}{2 a \cos 30 °} + \frac{1}{3 a \cos 30 °} - . . . . . \infty] k^{^} = \frac{μ_{0}}{4 π} I \frac{2 \sin 30^{°}}{a \cos 30^{°}} [1 - \frac{1}{2} + \frac{1}{3} - . . . . . \infty] k^{^} = \frac{μ_{0}}{4 π} I \frac{l n4}{\sqrt{3 a}} k^{^}$

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