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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:

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$\frac{π}{3 t}$

$\frac{2 π}{t}$

$\frac{2 π}{3 t}$

$\frac{π}{t}$

answer is B.

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Detailed 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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