In region `x gt 0` a uniform and constant magnetic field `vec(B)_(1) = 2 B_(0) hat(k)` exists. Another uniform and constant magnetic field `vec(B)_(2) = B_(0) hat(k)` exists in region `x lt 0` A positively charged particle of mass m and charge q is crossing origin at time t =0 with a velocity `bar(u) = u_(0) hat(i)`. The particle comes back to its initial position after a time : (`B_(0),u_(0)` are positive constants)

Options

A. `(3)/(2) (pi m)/(q B_(0))`
B. `(2 pi m)/(q B_(0))`
C. `(3 pi m)/(q B_(0))`
D. Particle does not come back to its initial position

Answer

B

Explanation

The motion of positively charged particle in the given combination of magnetic field will be as shown. The particle comes back to its initial position after covering three half circles.

Hence net time taken to come back to initial position is
`T = (pim)/(2 q B_(0))+(pi m)/(qB_(0))+(pi m)/(2qB_(0))=(2pi m)/(qB_(0))`