Magnetic Effects & Magnetism

JEE Main level, single correct, medium

126 of 276

Question 126 of 276

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E⃗\vec{E} and B⃗\vec{B} represent the electric and magnetic fields respectively, then the region of space may have :
(A) E=0,B=0E=0,B=0; (B) E=0,B≠0E=0,B\neq 0; (C) E≠0,B=0E\neq 0,B=0; (D) E≠0,B≠0E\neq 0,B\neq 0
Choose the most appropriate answer from the options given below :

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Answer: (C) (A), (B) and (D) only

Net force on proton inside an electric and a magnetic field is given by
F⃗e+F⃗m=qE⃗+q(v⃗×B⃗)...(1){\vec{F}}_{e}+{\vec{F}}_{m}=q\vec{E}+q\left(\vec{v}\times \vec{B}\right)...\left(1\right)
If both E⃗\vec{E} and B⃗\vec{B} are zero, then F⃗e{\vec{F}}_{e} and F⃗m{\vec{F}}_{m} both are zero. Hence, velocity may remain constant. Therefore, option (A) is correct.
If E=0,B≠0E=0,B\neq 0, but velocity is parallel or antiparallel to the magnetic field, then also F⃗e{\vec{F}}_{e} and F⃗m{\vec{F}}_{m} both are zero. Hence, option (B) is also correct.
If E≠0,B≠0E\neq 0,B\neq 0, but F⃗e+F⃗m=0{\vec{F}}_{e}+{\vec{F}}_{m}=0, then also velocity may remain constant. Thus, option (D) is also correct.

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