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

Options

A. `(mu_(0)Iqv)/(2pi d)`
B. `(mu_(0)Iqv)/(pi d)`
C. `(2mu_(0)Iqv)/(pi d)`
D. zero

Answer

D

Explanation

`B_(O) = (mu_(0)I)/(2pi.(d)/(2)) xx = (2mu_(0)I)/(pi d)` along `-z` -direction
`vec(B)_(O) = -(2 mu_(0)I)/(pi d) hat(k)`
`vec(v) = v_(0)hat(k)`
`vec(F)_(m) = qvec(v) xx vec(B) = 0`