JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Magnetic Effects of Current

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A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle:

(A) $1 : 1$
(B) $1 : 2$
(C) $2 : 1$ ✓ Correct
(D) $1 : 4$

Answer: (C)

Solution

The radius of a charged particle in a magnetic field is

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

. Thus

r \propto K E

. If kinetic energy increases to 4 times, the new radius is

r_{n} = r_{0} 4 = 2 r_{0}

. The ratio

\frac{r _{n}}{r _{0}} = 2 : 1

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Single correct option

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