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  4. A charged particle moves with constant velocity in a region where no effect of gravity is felt but an electrostatic field vecE together with a magnetic field vecB may be present. Then which of the following cases are possible ?

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Q. A charged particle moves with constant velocity in a region where no effect of gravity is felt but an electrostatic field $\vec{E}$ together with a magnetic field $\vec{B}$ may be present. Then which of the following cases are possible ?

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Solution:

If a charged particle is moving in a gravity-free space without changing its velocity, then three cases possible
(i) Particle can move with constant velocity in any direction, if $\vec{E}=0, \vec{B}=0$.
(ii) If $\vec{E}, \vec{B}$ are having values such that $q E=q v B$ and hence both forces (Force due to magnetic field and force due to electric field) acts in such a way that they cancel each other, in this case also particle can move with uniform velocity.
(iii) If $\vec{E}=0, \vec{B} \neq 0$ and $\vec{B}$ is such that it acts in the direction of velocity then magnetic force would be zero and hence velocity can remain constant.