Question

Two spheres carrying the charge
Q_{1}=+Q,Q_{2}=−Q uniformly distributed across the
surface have radii R_{1} and R_{2}, and their
centers are a distance dapart. We assume that
d>>R_{1},R_{2}. (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>>R_{1},R_{2}, 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, R_{2}, d and ε_{0}. (f) Show that in the
limit d→∞, the result reduces to that of two spherical capacitors
in series.

Answer #1

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