JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Magnetic Effects of Current

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Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is

6 : 5

and their respective masses ratio is

9 : 4

. Then, the ratio of their charges will be :

(A) $8 : 5$
(B) $5 : 4$ ✓ Correct
(C) $5 : 3$
(D) $8 : 7$

Answer: (B)

Solution

The radius of circular path in a magnetic field is:

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

where

K

is the kinetic energy.

Since kinetic energies are equal:

\frac{R _{1}}{R _{2}} = \frac{m _{1}}{q _{1}} \times \frac{q _{2}}{m _{2}}

Rearranging:

\frac{q _{1}}{q _{2}} = \frac{m _{1}}{m _{2}} \times \frac{R _{2}}{R _{1}} = \frac{9}{4} \times \frac{5}{6} = \frac{3}{2} \times \frac{5}{6} = \frac{5}{4}

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Magnetic Effects of Current

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