A charged particle moves in a gravity free space where an electric field of strength E and a magnetic field of induction B exist. State the following statements as True of False.
a. If `E pi 0 and B pi 0,` velocity of the particle may remain constant.
b. If `E = 0`, the particle cannot trace a circular path.
c. If `E=0`, kinetic energy of the particle remains constant.

Explanation

(a) True, (b) False, (c) True
A uniform megnetic field B and a uniform electric field E
exist perpendicular to each other and the particle moves along a
direction perpendicular to both these fields , then forces exerted
by these two fields may be opposite to each other. If magnitudes
of these forces are equal, then the resultant force on the particle
will become zero.
Hence, the particle will move with constant velocity. Hence,
(a) is correct. Obviously (b) is wrong.
If E is equal to zero then the particle will experience a force due
to magnetic field alone. But the force exerted by the magnetic
field is always perpendicular to the direction of its motion. Hence,
no power is associated with this forces. In other words, no work
is done by the magnetic field on the particle. Therefore, KE of
the particle will remain constant. Hence (c) is correct.