An electron with charge qe is at rest around a proton with charge qp, It is assumed that it orbits in a fixed orbit of radius R due to the Coulomb gravitational force between them. If the circularly moving electron is considered as a current loop, the system will be in a magnetic field of magnitude B oriented perpendicular to its momentum.

 

a) Find the linear velocity of the electron in terms of ke, me, R and q (|qe| = |qp| = q), where ke is the Coulumb constant and me is the mass of the electron.

 

b) Write down the period of the electron and the value of the resulting current in terms of ke, me, R and q.

 

c) Using the definition of current, calculate the resulting torque in terms of ke, me, R, R and q (|qe| = |qp| = q).