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, then the region of space may have:

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Solution

Q.
A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\bar{E}$ and $\bar{B}$ represent the electric and magnetic fields respectively, then the region of space may have:

(A) E = 0, B = 0 (B) E = 0, B ≠ 0

(C) E ≠ 0, B = 0 (D) E ≠ 0, B ≠ 0

Choose the most appropriate answer from the options given below: [2024]

1 (A), (B) and (C) only

2 (A), (C) and (D) only

3 (A), (B) and (D) only

4 (B), (C) and (D) only

Ans.
(3)

Net force on particle must be zero i.e.

$q \vec{E} + q \vec{V} \times \vec{B} = 0$

Possible cases are

(i) $\vec{E} and \vec{B} = 0$

(ii)   $\vec{V} \times \vec{B} = 0, \vec{E} = 0$

(iii)   $q \vec{E} = - q \vec{V} \times \vec{B}$

   $\vec{E} \neq 0 and \vec{B} \neq 0$

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