A magnetic field `vec B = B_0 hat j` exists in the region `a lt x lt 2a` and `vec B = - B_(0) hat i` in the region `2a lt x lt 3a`, where `B_0` is positive constant. A positive point charge moving with a velocity `vec v = v_0 hat i` where `v_0` is a positive constant, enters.


the magnetic field at x=a, The trajectory of the charge in this region can be like,

Options

A.
B.
C.
D.

Answer

A

Explanation

Force on the charge particles in a magnetic field `vec F = q (vec v xx vec B)`
In the region `a < x < 2a`, the force on the charge particles , must be in the direction of `hat i xx hat j` that is , in `+(z)` direction , which is vertically upward .And in the region `2a lt x lt 3a`, the force on the charged will bu in -z direction , which is vertically downwards.
For `a < x < 2a` path will be concave upward.
For `2a < xx < 3a`, path will be concave downward.
More, there should not be any kink in the path at x=2a. Hence graph (a) is correct,