JEE Main 2025 Apr 3 Shift 2, Physics Q20: Motion of a Charged Particle in a Magnetic Field

JEE Main2025Apr 3, Shift 2Physics

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

Assertion A : If oxygen ion (O $^{- 2}$ ) and Hydrogen ion (H $^{+}$ ) enter normal to the magnetic field with equal momentum, then the path of O $^{- 2}$ ion has a smaller radius of curvature than that of H $^{+}$ .

Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

In the light of the above statement, choose the correct answer from the options given below

A
A is true but R is false
B
Both A and R are true but R is NOT the correct explanation of A
C
A is false but R is true
D
Both A and R are true and R is the correct explanation of A

Solution

For a charged particle moving perpendicular to a uniform magnetic field,

$r = \frac{p}{∣ q ∣ B}$

Assertion (A):

For equal momentum,

$r_{O^{2 -}} = \frac{p}{2 e B} = \frac{1}{2} r_{H^{+}}$

$∴$ The $O^{2 -}$ ion has a smaller radius of curvature.

Hence, Assertion is True.

Reason (R):

A proton and an electron have the same magnitude of charge $(e)$ .

For equal momentum,

$r = \frac{p}{e B}$

$∴$ Both have the same radius of curvature (only the direction of motion is opposite).

Hence, Reason is False.

Answer: Assertion is True, Reason is False.

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JEE Main 2025 Apr 3 Shift 2, Physics Q20: Motion of a Charged Particle in a Magnetic Field

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