Debye lenght

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Consider Debye’s potential created by a punctual test charge \(q_T\) that is placed inside an homogeneous plasma.

a) Show that the charge in the shielding cloud exactly cancels \(q_T\). Calculate the total charge inside spheres of radii \( \lambda_D/2 , \; \lambda_D\) and \( 5\lambda_D \)

b)Determine the electrostatic interaction energy between the test charge and the particles in the plasma and the total mean energy of the plasma particles (assume \( T_e=T_i=T\) ).