Question

If $E$ and $B$ are the magnitude of electric and magnetic field respectively in some region of space, then the possibilities for which a charged particle may move in that space with a uniform velocity of magnitude$v$ are

(A) $E = vB$
(B) $E \ne 0,\;B = 0$
(C) $E = 0,\;B \ne 0$
(D) $E \ne 0,\;B \ne 0$

Answer 1

For the determination of the write answer, use the information related to the electric field's properties and magnetic field. They can produce electric charges when they are moving or remain in the stationary position.

Complete step by step answer:
The electric field is that region where we can observe that the electric charge is experiencing some electric force. Due to the electric force's effect, the electric field's motion gets affected, and the charge tends to change its state of motion. The magnetic field is the space around the current-carrying conductor around which we can experience magnetic effects. It can also affect the motion of the electric charge.

If the magnitude of the electric and magnetic field is almost equal, then a balanced condition can occur where the motion of the charged particles does not affect, and for this condition, the relation between electric and magnetic field is $E = vB$, here $E$ is the electric field, $B$ is the magnetic field and $v$ is the velocity of the charge. So option (A) is correct.

If the electric field's magnitude is zero, but the magnetic field exists in the space, then the charge is not affected by the electric field, but the charge's motion gets affected by the magnetic field. The magnetic field tends to change its motion direction but cannot change its velocity, so the charge can move with uniform velocity in the space, if $E = 0$ and$B \ne 0$.Therefore option (C) is correct.

When both fields are not present in the space where the charge is moving, then the charge's motion becomes uniform, and the charge can move with uniform velocity in the space. So, option (D) is also correct.
Therefore, if $E$ and $B$ are the electric and magnetic field magnitudes respectively in some region of space, then the possibilities for which a charged particle may move in that space with a uniform velocity of magnitude $v$ are $E = vB$, $E = 0,\;B \ne 0$ and $E \ne 0,\;B \ne 0$

So, the correct answers are “Option A,C and D”.

Note:
The option (D) is incorrect because in option (B) the magnitude of the electric field is not zero. We know that the electric field can influence the motion of the charged particles by exerting electric force and due to this, the charge particles cannot move with uniform velocity.