Winding around a pole a with a conducting spring.

Electricity and Magnetism Level 4

A laminar body of mass m made of insulating material carrying some amount of charge is attached (welded) to one end of a extremely strong and very stretchable spring of almost zero equilibrium length. The other end of which is fixed wound to fixed non conducting pole and then grounded. The spring constant initially is K. Initial conditions are set up so the mass moves around a cylindrical pole of radius a on a frictionless horizontal table. L is the initial distance from the centre of mass to the pole.We start by giving a velocity to the lamina as shown. The spring winds around the pole and the lamina eventually hits the pole . What amount of charge in\[\mu C \] is lost from the lamina at half of the total time before collision if the electrostatic potential at the centre of the pole at that time is V.The spring is made of conducting material of resistance R
Neglect any sort of electrostatic interactions or energy/

\[K=3*10^{20}N/m \]

\[m=5kg \]

\[R=3m\Omega \]

\[a=0.05m \]

\[V=2V \]

\[L=20m \]

assume \[a\ll L \] find (the required charge in micro C) + 10.11 as the final answer


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