Q155 / 155 · WBJEE 2020 · Physics

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

  • Correct answer
    A
    $\vec{E} \neq 0, \vec{B} \neq 0$
  • B
    $\vec{E} \neq 0, \vec{B}=0$
  • Correct answer
    C
    $\vec{E}=0, \vec{B}=0$
  • Correct answer
    D
    $\overrightarrow{\mathrm{E}}=0, \overrightarrow{\mathrm{B}} \neq 0$

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.

Hence, the correct answer is options: 'A', 'C', 'D'.

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