Question

Let C be a positively oriented circle centered at the origin with radius R>1.

a) Confirm your result for n=2 by using Cauchy's Residue Theorem.

Answer 1

The question involves calculating electric potential in different regions around two charged concentric spheres. A full calculation requires more specific information, but general principles involving electric potentials due to spherical charge distributions allow for a qualitative explanation.

Step-by-step explanation:

The student's question pertains to electric potential in different regions around two concentric spheres with radii R₁ and R₂ and with positive charges q₁ and q₂, respectively. To answer this, we would calculate the electric potential in each region by using the known expressions for the electric potential due to a point charge and employing the principle of superposition.

However, as the question references figures and other information that isn't provided in the prompt, a complete step-by-step calculation cannot be given. Typically, for regions inside the inner sphere (r < R₁), only the charge within that radius contributes to the potential. For regions between the spheres (R₁ < r < R₂), the potential is due to both charges, q₁ and q₂. For regions outside the outer sphere (r > R₂), the potential would be as if all charge were concentrated at the center, due to both charges. These explanations are in line with the electric potential due to spherical charge distributions.