### Magnetic Effects Of Current Question 4

#### Question 4 - 2024 (27 Jan Shift 1)

A proton moving with a constant velocity passes through a region of space without any change in its velocity.

If $\overrightarrow{E}$ and $\overrightarrow{B}$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $E=0, B=0$

(B) $E=0, B \neq 0$

(C) $E \neq 0, B=0$

(D) $E \neq 0, B \neq 0$

Choose the most appropriate answer from the options given below :

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

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

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

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

## Show Answer

#### Answer: (3)

#### Solution:

Net force on particle must be zero i.e. $q \vec{E}+q \vec{V} \times \vec{B}=0$

Possible cases are

(i) $\overrightarrow{E} \& \overrightarrow{B}=0$

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

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

$\overrightarrow{E} \neq 0 \& \overrightarrow{B} \neq 0$