Question 13

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\vec{E}$$ and $$\vec{B}$$ 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 :

A proton moves with constant velocity, meaning the net force on it is zero.

(A) $$E = 0, B = 0$$: No force, proton moves at constant velocity. Possible.

(B) $$E = 0, B \neq 0$$: If the proton moves parallel to $$\vec{B}$$, the magnetic force $$q\vec{v} \times \vec{B} = 0$$. Possible.

(C) $$E \neq 0, B = 0$$: The electric force $$q\vec{E} \neq 0$$, so the proton would accelerate. Not possible.

(D) $$E \neq 0, B \neq 0$$: If $$q\vec{E} + q\vec{v} \times \vec{B} = 0$$, the electric and magnetic forces can cancel. Possible.

The correct options are (A), (B) and (D) only, which corresponds to Option (3).

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