Given below are two statements: one is labelled as Assertion A and… | JEE Main 2025 (3 Apr, Shift 2)

Q20JEE Main 2025 · 3 APR · SHIFT 2Medium

Moving Charge in a Magnetic Field

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

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 statements, choose the correct answer from the options given below

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Answer: (c)

$r = \dfrac{p}{qB}$ , so for equal momentum $r \propto \dfrac{1}{q}$ .
A: $|q_O| = 2e$ , $q_H = e \Rightarrow r_O = \dfrac{r_H}{2}$ . The $\text{O}^{2-}$ path has the smaller radius of curvature (so actually the larger curvature $1/r$ ).
R: proton and electron have the same $|q| = e$ , so with equal momentum their radii are equal. R is false.
Taking A to mean the O ion has the smaller radius of curvature, A is true and R is false.
So the answer is (c).

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