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  4. 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 ≠ 0 (3) E ≠ 0, B ≠ 0 (4) E ≠ 0, B=0

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Q. 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) $E=0, B \neq 0$
(3) $E \neq 0, B \neq 0$
(4) $E \neq 0, B=0$

BHUBHU 2006

Solution:

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