A magnetic field ` vec(B) = B_(0)hat(j)` , exists in the region `a ltxlt2a` , and `vec(B) = -B_(0) hat(j)` , in the region `2a lt xlt 3a`, where `B_(0)` is a 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

In the given situation the magnetic field is as follows:
`vec B = B_(0) jat j ` in the region `a lt x lt 2a " and " vecB = - B_(0) hat j `, in the region `2a lt x lt 3a`
And also velocity is along positive X - axis, `vecv = v_(0) hat i`
The magnetic force on the charged particle is given by :
`vec F = q ( vec v xx vec B)`
In the region `a lt x lt 2a`, the magnetic force will be directed along positive Z-axis, making the shape of its path concave upwards. Whereas, in the region the `2a lt x lt 3a` the direction of the magnetic force will be along the negative Z-axis, making the shape of its path concave downwards.
Hence option (a) is correct.