JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Magnetic Effects of Current

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Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii

R_{1}

and

R_{2}

respectively. The mass ratio of X and Y is :

(A) $(\frac{R _{2}}{R _{1}})^{2}$
(B) $(\frac{R _{1}}{R _{2}})^{2}$ ✓ Correct
(C) $(\frac{R _{1}}{R _{2}})$
(D) $(\frac{R _{2}}{R _{1}})$

Answer: (B)

Solution

A charged particle accelerated through potential

V

gains kinetic energy

q V = \frac{1}{2} m v^{2}

, so

v = 2 q V / m

. Once it enters the magnetic field, its circular radius is

R = \frac{m v}{q B} = \frac{2 m q V}{q B}

Since

q

V

and

B

are the same for both particles,

R \propto m

, which means

m \propto R^{2}

\frac{m _{X}}{m _{Y}} = (\frac{R _{1}}{R _{2}})^{2}

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Single correct option

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JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Magnetic Effects of Current

Solution

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