JEE Main · 2005 · 08 May 2005 · Offline · Magnetic Effects of Current

A charged particle of mass

m

and charge

q

travels on a circular path of radius

r

that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is

(A) $\frac{2 π m q}{B}$
(B) $\frac{2 π q ^{2} B}{m}$
(C) $\frac{2 π q B}{m}$
(D) $\frac{2 π m}{q B}$ ✓ Correct

Answer: (D)

Solution

The magnetic force supplies the centripetal force,

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

, which gives the angular speed

ω = \frac{v}{r} = \frac{q B}{m}

. The period is then

T = \frac{2 π}{ω} = \frac{2 π m}{q B}

, independent of the particle's speed and radius.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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