Question

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

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

Answer 1

Answer: (B)

proton trajectory is less curved

let, momentum of electron and proton be p.
Transverse electric force on particle provides the centripetal force to support the circular motion.
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 = $\frac{p^2}{mqE}$

where, $p=momentum=mv$

Given $q$ ,$p$ and $E$ are constant. So, we can say that $r\propto \frac{1}{m}$

Radius of curvature is higher for a lighter mass particle which is an electron and vice versa for proton.