JEE Main 2022 · 24 June · morning · Single correct · +4 / −1
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.
- (a) Both (A) and (R) are true and (R) is the correct explanation of (A).
- (b) Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
- (c) (A) is true but (R) is false.
- (d) (A) is false but (R) is true.
Answer and solution
Answer (a) Both (A) and (R) are true and (R) is the correct explanation of (A).
Solution
Physics sir · 4 steps
A force that always acts sideways to the motion can turn the charge, but it can never speed it up.
- Check the Reason. The magnetic force is F⃗ = q v⃗ × B⃗. A cross product is perpendicular to both vectors, so F⃗ is always perpendicular to v⃗. (R) is true.
- Power is zero. The rate at which a force does work is F⃗ · v⃗. With F⃗ perpendicular to v⃗, this dot product is zero at every instant.
P = F⃗ · v⃗ = q(v⃗ × B⃗) · v⃗ = 0
- Check the Assertion. No work is done, so by the work-energy theorem the kinetic energy 1/2mv² stays constant, and so does the speed. Only the direction of velocity changes, which is why the path is a circle or a helix. (A) is true.
- So. (A) follows directly from (R): the force is perpendicular, so it does no work, so speed and energy stay the same. The answer is (a).
The idea to keep. A magnetic field alone never changes a charge's speed or kinetic energy, because F⃗ ⊥ v⃗ means zero work. It only bends the path. To change the speed you need an electric field.
Answer from the NTA final answer key. Solution by PrepWiser.