Q. What will be the resultant magnetic field at origin due to four infinite length wires if each wire produces magnetic field ‘$B$’ at origin
A) 4 $B$
B) $\sqrt{2}\ B$
C) $2\sqrt{2}\ B$
D) Zero
Explanation
(c) Direction of magnetic field $(B_{1},\ B_{2},\ B_{3}$ and $B_{4}$) at origin due to wires 1, 2, 3 and 4 are shown in the following figure
$B_{1} = B_{2} = B_{2} = B_{4} = \frac{\mu_{0}}{4\pi}.\frac{2i}{x} = B.$ So net magnetic field at origin $O$
$B_{net} = \sqrt{\left( B_{1} + B_{3} \right)^{2} + \left( B_{2} + B_{4} \right)^{2}} = \sqrt{(2B)^{2} + (2B)^{2}} = 2\sqrt{2}B$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.