Q. A current ‘I’ is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5m apart, in the negative Z-direction. A point P is at a perpendicular distance 3m from the first wire and 4 m from the second. What will be magnitude of the magnetic field $\vec{B}$ at P?
Solution:
$B_{1}=magnetic field due to first wire =\frac{\mu_{0}\times I}{2\pi\times3}$
$B_{2}=magnetic field due to second wire =\frac{\mu_{0}\times I}{2\pi\times4}$
$B=net magnetic field =\sqrt{B_{1}^{2}+B_{1}^{2}}=\frac{\mu_{0}I}{2\pi}\sqrt{\frac{1}{9}+\frac{1}{16}} =\frac{\mu_{0}I\times5}{2\pi\times3\times4}=\frac{5}{24}\times\frac{\mu_{0}I}{\pi}$
$B=\frac{5}{24\pi} \mu_{0}I ;but the exact answer is not given, so best possible answer is C$
