A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec E$ and $\vec B$ represent the electric and magnetic fields respectively, then the region of space may have:
(A) $E = 0,\ B = 0$; (B) $E = 0,\ B \ne 0$; (C) $E \ne 0,\ B = 0$; (D) $E \ne 0,\ B \ne 0$
Choose the most appropriate answer from the options given below:
Answer: (C) (A), (B) and (D) only
The velocity is unchanged, so the net force $q(\vec E + \vec v\times\vec B)$ must be zero.
(A) No fields: no force. Possible.
(B) $E = 0$, $B \ne 0$: no force if $\vec v$ is parallel to $\vec B$. Possible.
(C) $E \ne 0$, $B = 0$: the force $q\vec E$ cannot vanish. Not possible.
(D) Both non-zero: possible when $\vec E = -\vec v\times\vec B$ (crossed fields, as in a velocity selector).
Hence (A), (B) and (D) only.
Solution by Sreeraj P, M.Sc Physics