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Q.

Two very long straight parallel wires carry steady currents I and –I. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is

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a

$\frac{μ_{0} Iqv}{2 πd}$

b

$\frac{μ_{0} Iqv}{πd}$

c

$\frac{2 μ_{0} Iqv}{πd}$

d

zero

answer is D.

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Detailed Solution

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As the direction of currents in the wires are in opposite directions, so, the net magnetic field at the point equidistant from the wires will be double of the field due to individual wires and the direction the field will be perpendicular of the plane of the wire. So, the field and the velocity of the charge are along the same line. Hence, force on the charge will be zero.

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Two very long straight parallel wires carry steady currents I and –I. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is