# The region between x = 0 and x = L is filled with uniform steady magnetic field B0k. Aparticle of mass m, positive charge q and velocity V0i travels along x-axis and enters the region of the magnetic field. Neglect the gravity throughout the question. (a) Find the value of L is fthe particle emerges from the region of magnetic field with its final velocity at an angle 300 to its initial velocity. (b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the magnetic field now expands upto 2.1 L.

ROSHAN MUJEEB
4 years ago
As the initial velocity of the particle is perpendicular to the field, the particle will move along the arc of a circle as shown If r is the radius of the circle, then
mv20r=qv0B0⇒r=mv0qB0

Also, from geometry,L=rsin30∘⇒r=2LL=rsin30∘⇒r=2L
orL=r2=mv02qB0
(b) In this case, x=2.1mv02qB0>r
Hence, the particle will complete semicircle path and emerge from the field with velocity −v0iˆ as shown in Fig. Time spent by the particle in the magnetic field T=πrv0=πmqB0
The speed of the particle does not change due to magnetic field.