Question

The mass of a proton is $1847$ times that of an electron. A electron and a proton are injected into a uniform electric field at right angle to the direction of the field with the same initial K.E.

• A. The electron trajectory will be less curved than the proton trajectory
• B. Both the trajectories will be straight
• C. The proton trajectory will be less curved than the electron trajectory
• D. Both the trajectories will be equally curved

Answer 1

Answer: (D)

Both the trajectories will be equally curved

$K=\frac{1}{2}m{V}^2$. In electric field,
$Y=\frac{qE{x}^2}{2m{V}^2}=\frac{qE{x}^2}{4K}$
The curvature of the trajectory is proportional to $qE/K$. Since q, E and K are same for both particles, have the trajectories will have the same curvature.