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JEE Main 2024 (27 Jan, Shift 1) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from JEE Main 2024 (27 Jan, Shift 1)

Q39JEE Main 2024 · 27 JAN · SHIFT 1Medium

Moving Charge in a Magnetic Field

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)

  1. (A) E=0,B=0E = 0, B = 0: no force, velocity unchanged. Possible.
  2. (B) E=0,B≠0E = 0, B \neq 0: possible if v⃗∥B⃗\vec{v} \parallel \vec{B}, since then qv⃗×B⃗=0q\vec{v} \times \vec{B} = 0.
  3. (C) E≠0,B=0E \neq 0, B = 0: force qE⃗q\vec{E} always changes the velocity. Not possible.
  4. (D) E≠0,B≠0E \neq 0, B \neq 0: possible with crossed fields where qE⃗=−qv⃗×B⃗q\vec{E} = -q\vec{v} \times \vec{B}.
  5. So the answer is (c) (A), (B) and (D) only.
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