A particle of mass m and negative charge of magnitude q travels with a uniform velocity v and enters a region of magnetic field B , as shown in the figure. Determine the radius of the arc, the angle subtended by the arc at the centre, and the time the particle stays inside the magnetic field, respectively.

Step-by-step solution

Let the boundary of the magnetic field be the x-axis and the normal to it be the y-axis. The particle enters the magnetic field at the origin (0,0) . The velocity of the particle makes an angle with the vertical (y-axis). From the figure, the velocity vector is directed downwards and to the right. Thus, the initial velocity is: v = v i - v j The magnetic field is directed into the page: B = -B k The magnetic force on the negatively charged particle is: F = -q( v B ) = -q[(v i - v j ) (-B k )] F = -q(-vB ( i k ) + v