Two metallic spheres having charges q₁ and q₂ and radii a and b respectively are kept far apart and are joined with a conducting wire. The total charge on them is Q. What is the potential of each sphere?

Question

Accepted Answer

(3) (KQ)/(a+b). Given: spheres of radii a and b, far apart, joined by a wire; total charge Q. Idea: the wire makes the two spheres one conductor, so they settle at the same potential V. Being far apart, each behaves like an isolated sphere. For an isolated sphere V=(Kq)/r, so the charges become q₁=(Va)/K and q₂=(Vb)/K. Charge is conserved: q₁+q₂=(V(a+b))/K=Q. So V=(KQ)/(a+b) — as if the whole charge sat on one sphere of radius a+b.

Two metallic spheres having charges q₁ and q₂ and radii a and b respectively are kept far apart and are joined with a conducting wire. The total charge on them is Q. What is the potential of each sphere?

Step-by-step solution

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