JEE Main 2025 · 24 January · evening · 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) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :
- (a) (A) is true but (R) is false
- (b) Both (A) and (R) are true and (R) is the correct explanation of (A)
- (c) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
- (d) (A) is false but (R) is true
Answer and solution
Answer (b) Both (A) and (R) are true and (R) is the correct explanation of (A)
Solution
Physics sir · 4 steps
Magnetic force needs an angle between v and B. Line them up and the force vanishes.
- Magnetic force. On a charge q moving with velocity v⃗ in a field B⃗, the force is F⃗ = q v⃗ × B⃗. Its size depends on θ, the angle between v⃗ and B⃗.
F = |q| vB sin θ
- Check the Reason. If B⃗ is along v⃗, then θ = 0 and sin 0 = 0, so F = 0. With no force, the electron has no acceleration, so its velocity keeps the same size and direction.
- Check the Assertion. An electron moving at constant velocity in a uniform magnetic field is possible, and a field along the velocity is exactly the case that makes it happen. So (A) is true.
- So. Both statements are true, and (R) gives the reason the magnetic force is zero, which is what keeps the motion straight and uniform. The answer is (b).
The idea to keep. The magnetic force is zero whenever v⃗ is parallel or antiparallel to B⃗. Then the charge goes straight through at constant velocity, whatever its sign.
Answer from the NTA final answer key. Solution by PrepWiser.