A particle of mass m and charge q moves with a constant velocity v along the positive `x-` direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from `x=a` to `x=b`. The minimum value of v required so that the particle can just enter the region `xgtb` is

Options

A. `(q(b-a)B)/m`
B. `(qaB)/m`
C. `(q(b+a)B)/m`
D. `(qbB)/m`

Answer

A

Explanation

When the particle enters the transervse magnetic field, it describes a circular path of r, which is given by `(mv^(2))/r=qvBtherefore v=(qBr)/m` For v to be mnimum, r should be minimum and minium r, is (b-a). `therefore v=(qB(b-a))/m`.