First slide

Motion of a charged particle

Question

An $α$ particle is moving along a circle of radius R with a constant angular velocity . Point A lies in the same plane at a distance 2R from the centre. The point A records magnetic field produced by $α$ particle. If the minimum time interval between two successive times at which A records zero magnetic field is ‘t’, the angular speed $ω$ , in terms of t is:

Moderate

A

$\frac{2 π}{t}$
B

$\frac{2 π}{3 t}$
C

$\frac{π}{3 t}$
D

$\frac{π}{t}$

Solution

‘A’ records zero magnetic field when $α$ particle is moving on a line which passes through A, which happen when tangent to path passes through A. Angle covered between two such point B and $C = \frac{2 π}{3}$ as shown in figure.
Time taken to go from B to C is given as
$t = \frac{T}{3} = \frac{2 π}{ω} (\frac{1}{3})$
$\Rightarrow ω = \frac{2 π}{3 t}$

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