Question

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

• A. $\frac{{\mu }_{0}I\ln 2}{4\pi \sqrt{3}a}\hat{k}$
• B. $\frac{{\mu }_{0}I\ln 4}{4\pi \sqrt{3}a}\hat{k}$
• C. $\frac{{\mu }_{0}I\ln 2}{4\pi \sqrt{3}a}(-\hat{k})$
• D. zero

Answer 1

The correct option is B $\frac{{\mu }_{0}I\ln 4}{4\pi \sqrt{3}a}\hat{k}$

Magnetic field due to sequence of wires in parallel to each other is given by

$B=\frac{{\mu }_I}{4\pi }\left(\frac{2\sin {30}^{\circ }}{\cos {30}^{\circ }}\right)(\frac{1}{a}-\frac{1}{2a}+\frac{1}{3a}........\infty )$

$\Rightarrow B=\frac{{\mu }_{0}I}{4\pi \sqrt{3}a}\left(2\ln 2\right)\hat{k}=\frac{{\mu }_{0}I}{4\pi a\sqrt{3}}\ln 4\hat{k}$

Hence, option (b) is the correct answer.