Two very long straight, parallel wires carry steady currents $I_{1}$ and $I_{2}$ respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from both wires on the perpendicular line joining the two wires. The instantaneous velocity $\vec{v}$ is perpendicular to the plane of wires. The magnitude of force due to the magnetic fields of the two wires is (F) then the correct option(s):-

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$I_{1} = I, I_{2} = I$ in same direction, $F = \frac{2 μ_{0} I_{2} V}{π d}$

$I_{1} = I, I_{2} = I$ in opposite direction, $F = \frac{2 μ_{0} I_{2} V}{π d}$

$I_{1} = I, I_{2} = 2 I$ in same direction, $F = 0$

$I_{1} = 2 I, I_{2} = I$ in opposite direction, $F = 0$

answer is C, D.

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Detailed Solution

$\vec{F} = q (\vec{v} \times \vec{B}) a n d \vec{v} ‖ \vec{B}$

$s o, F = 0$

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