A charge ‘q’ moving along the X-axis with a velocity u is subjected to a uniform magnetic field B acting along z-axis as it crosses the origin.
(i) Trace it trajectory.
(ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer.

Solution

Given,
Charge is moving along the x-axis and,
Magnetic field is moving along z-direction.

Therefore, the magnetic force is such that the particle will follow a circular motion.
$F_{m} = q (\overset{⇀}{v} \times \overset{⇀}{B}) = q (V \overset{⏜}{i} \times B \overset{⏜}{k}) = - qVB \overset{⏜}{k} \overset{⏜}{y}$

Since, the force and velocity are perpendicular to each other, the particle does not gain energy.
W = $\overset{⇀}{F} . \overset{⇀}{v} = F v \cos θ$ [ $θ = 90^{o}$ ]

Hence, the force will not cause any change in velocity.