Question

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $E$ and $B$ represent the electric and magnetic fields respectively this region of space may have :
(1) $E=0,B=0$
(2) $E=0,B\ne 0$
(3) $E\ne 0,B\ne 0$
(4) $E\ne 0,B=0$

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 are correct
• D. 1, 2 and 3 are correct

Answer 1

Answer: (D)

If both $E$ and $B$ are zero, then ${\vec{F}}_e$ and ${\vec{F}}_m$ both are zero.
Hence, velocity may remain constant. If $E=0,B\ne 0$ but velocity is parallel or antiparallel to magnetic field, then ${\vec{F}}_e$ and ${\vec{F}}_m$ both are zero.
If $E\ne 0,B\ne 0$ but ${\vec{F}}_e+{\vec{F}}_m=0$, then also velocity may remain constant.