Two electrons each of charge e and mass m are attached one at each end of a light rigid rod of length 2r.The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. What is the angular momentum about the axis of rotation to the magnetic dipole moment of the system?




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Let the constant angular speed of rotation of the rod be ω.

The moment of inertia of the rod is zero because its mass is zero.

Moment of inertia of the two electrons about the axis of rotation is =
            I = Σ m r²  = m r² + m r² = 2 m r²

Angular momentum of the system = M = I ω = 2 m ω r²

Magnetic dipole moment of the system of two electrons and the rod: 
     p = 2 r e

The ratio =  2 m ω r² / 2 r e = m r ω