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MCQEasyJEE 2025Force on Moving Charge

JEE Physics 2025 Question with Solution

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A): An 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:\text{In the light of the above statements, choose the correct answer from the options given below:}

  • A

    Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

  • B

    (A) is false but (R) is true

  • C

    Both (A) and (R) are true and (R) is the correct explanation of (A)

  • D

    (A) is true but (R) is false

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: An electron moves with constant velocity in a straight line in a uniform magnetic field.

Find: Which option correctly evaluates Assertion (A) and Reason (R).

For a charged particle in a magnetic field, the magnetic force is

F⃗=q(v⃗×B⃗)\vec{F} = q(\vec{v} \times \vec{B})

If the electron moves in a straight line with constant velocity, the net magnetic force must be zero.

This happens when the angle between v⃗\vec{v} and B⃗\vec{B} is 0∘0^\circ or 180∘180^\circ, so that

v⃗×B⃗=0\vec{v} \times \vec{B} = 0

Hence the magnetic field can be along the direction of velocity of the electron, and the electron will continue to move in a straight line with constant velocity.

Therefore, Assertion (A) is true and Reason (R) is also true. The reason correctly explains the assertion.

The correct option should be C.

However, the solution marks A as correct, which is inconsistent with the magnetic force law and the given statements.

Common mistakes

  • Assuming that magnetic force can act along the direction of motion. This is wrong because magnetic force is always perpendicular to both v⃗\vec{v} and B⃗\vec{B}. Use F⃗=q(v⃗×B⃗)\vec{F} = q(\vec{v} \times \vec{B}) and check when the cross product becomes zero.

  • Thinking that straight-line motion in a magnetic field is impossible. This is wrong because if v⃗\vec{v} is parallel or antiparallel to B⃗\vec{B}, then the magnetic force is zero. In that case, the particle can continue in a straight line with constant speed.

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