Question

An electron and a proton are injected into a uniform magnetic field perpendicular to it with the same momentum. If the two particles are injected into a uniform transverse electric field with same kinetic energy, then

• A. electron trajectory is more curved
• B. proton trajectory is more curved
• C. both trajectories are equally curved
• D. both trajectories are straight lines

Answer 1

Answer: (C)

both trajectories are equally curved

Let, Kinetic energies of electron and proton be K.
Transverse electric force on particle provides the centripetal force to support the circular motion in this case.
If r is radius of curvature, $F_e=F_c$

i.e. qE = m $\frac{v^2}{r}$.

Solving the above equation we get r = $\frac{2K}{qE}$ where K = Kinetic Energy = $\frac{m{v}^2}{2}$

Here, q,E and K are constant. So, radius of curvature is same for both of them.