Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If oxygen ion (\(\text{O}^{-2}\)) and Hydrogen ion (\(\text{H}^{+}\)) enter normal to the magnetic field with equal momentum, then the path of \(\text{O}^{-2}\) ion has a smaller curvature than that of \(\text{H}^{+}\). 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

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

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

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Magnetic Effects of Current

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 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✓ Correct
(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

Answer: (A)

Solution

The radius of the circular path in a magnetic field is

r = \frac{m v}{q B} = \frac{p}{q B}

, fixed by the momentum and the charge alone. For equal momentum the oxygen ion

O^{- 2}

, carrying charge

2 e

, follows a path of radius half that of

H^{+}

with charge

e

; its circular path is the tighter, smaller one, so the assertion holds. A proton and an electron, however, carry the same magnitude of charge, so with equal momentum they trace paths of equal radius rather than the proton's being smaller, and the reason fails. The assertion is true while the reason is false.

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Magnetic Effects of Current

Solution

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