Question

# Two spheres carrying the charge Q1=+Q,Q2=−Q uniformly distributed across the surface have radii R1 and R2,...

Two spheres carrying the charge Q1=+Q,Q2=−Q uniformly distributed across the surface have radii R1 and R2, and their centers are a distance dapart. We assume that d>>R1,R2. (a) Why is this assumption necessary? (b) Choose a coordinate axis along the direction that connects the centers of the two spheres.Choosethe origin at the center of sphere 1. This defines the radial direction. In unit vector notation, what is the net electric field at some point P between the surfaces of the two spheres along the chosen radial
direction? (c) From the electric field, find the potential difference between the surfaces of the spheres. (d) With d>>R1,R2, to what simpler form can the potential difference found at (c) be reduced? (e) From this potential difference, derive the capacitance of the system in terms of R1, R2, d and ε0. (f) Show that in the limit d→∞, the result reduces to that of two spherical capacitors in series.

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