JEE Main · 2012 · 29 Apr 2012 · Offline · Magnetic Effects of Current

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Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively

r_{p}, r_{d}

and

r_{α}

. Which one of the following relations is correct?

(A) $r_{α} = r_{p} = r_{d}$
(B) $r_{α} = r_{p} < r_{d}$ ✓ Correct
(C) $r_{α} > r_{d} > r_{p}$
(D) $r_{α} = r_{d} > r_{p}$

Answer: (B)

Solution

In a magnetic field a particle of kinetic energy

K

moves on a circle of radius

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

, so for equal

K

the radius goes as

\frac{m}{q}

. Taking the proton as the unit, the deuteron has twice the mass and the same charge, giving

r_{d} = 2 r_{p}

, while the alpha particle has four times the mass and twice the charge, giving

r_{α} = \frac{4}{2} r_{p} = r_{p}

. Hence

r_{α} = r_{p} < r_{d}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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JEE Main · 2012 · 29 Apr 2012 · Offline · Magnetic Effects of Current

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