JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Magnetic Effects of Current

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A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius(r). Which of the following curves represents the variation of

r

with

E

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

A charged particle in a magnetic field moves on a circle of radius

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

, while its kinetic energy is

E = \frac{1}{2} m v^{2}

, giving

v = 2 E / m

. Substituting,

r = \frac{2 m E}{q B}

, so

r \propto E

. The correct graph therefore starts at the origin and rises as a square-root curve — concave down, with its slope decreasing as

E

increases.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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