JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Magnetic Effects of Current

A proton, a deuteron and an

α

particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is ____ and their speed is ____ in the ratio.

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

Answer: (A)

Solution

All three particles carry the same momentum

p

, so each moves at

v = \frac{p}{m}

and the magnetic force becomes

F = q v B = \frac{q}{m} pB

which depends on the charge to mass ratio. Taking the proton as

(e, m)

, the deuteron is

(e, 2 m)

and the

α

particle is

(2 e, 4 m)

, so

F_{p} : F_{d} : F_{α} = \frac{e}{m} : \frac{e}{2 m} : \frac{2 e}{4 m} = 2 : 1 : 1

The speeds follow from

v = \frac{p}{m}

alone:

v_{p} : v_{d} : v_{α} = \frac{1}{m} : \frac{1}{2 m} : \frac{1}{4 m} = 4 : 2 : 1

The magnetic forces are in the ratio

2 : 1 : 1

and the speeds in the ratio

4 : 2 : 1

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Magnetic Effects of Current

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