A very long straight wire carries a current I. At the instant when a charge `+Q` at point `P` has velocity `vecV`, as shown, the force on the charge is

Options

A. Opposite to ox
B. along ox
C. opposite to oy
D. along oy

Answer

D

Explanation

AT point P, Maxwell cork skew rule defines the direction of magnetic field and Fleming's left hand rule reveal the concept of force on the charge in this field.
According to Maxwell's cork screw rule the direction of magnetic field at point P in plane of paper is perpendicular to the plane of paper inwards i.e., along z-direction. Now since charge is moving along x-direction therefore, from fleming's left hand rule stretching the forefinger in direction of paper inwards the thumb will indicate the direction of force F acting on the charged particle along oy.
Alternate: As discussed above, B acts inward into plane of the paper and v is along ox hence.
`F=Q(vec(v)xxvec(B))=Q|(hati,hatj,hatk),(v,0,0),(0,0,-B)|`
`=Q[hati(0)-hatj(-vB)+hatk(0)]`
`=+hatjQvB`
i.e. force is along oy direction.