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  • Two particles each of mass m and charge q, are attached to the two ends of a light rigid rod of length  . The rod is rotated at a consta

Two particles each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2 {l} . The rod is rotated at a constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

Option: 1

\mathrm{\frac{q}{2 m} }


Option: 2

\mathrm{\frac{q}{m} }


Option: 3

\mathrm{\frac{2 q}{m} }


Option: 4

\mathrm{\frac{q}{\pi m}}


Answers (1)

best_answer

According to Ampere's Law, the magnetic moment of a current I flowing in a circular path of area of cross-section A is given by

\mathrm{\mu_m =I A \\ }

{ =\frac{q}{T} A=\frac{q \pi(2 l)^2}{T} }

It is given that the charge q is moving in a circular path of radius 2 l. Therefore, the time period {T= 2~ \pi(2 l) / v } . Hence

{\mu_m=\frac{q v}{2 \pi(2 l)} \times \pi(2 l)^2=q v l }

The angular momentum { L=m v(2 l) } .

Therefore,
{ \frac{\mu_m}{L}=\frac{q v l}{m v(2 l)}=\frac{q}{2 m}, \text { which is choice (a). } }

Posted by

Irshad Anwar

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