Question:
Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfacesof the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.
Answer:
Let a be the radius of a sphere A, QA be the charge on the sphere, and CA be the capacitance of the sphere. Let b be the radius of a sphere B, QB be the charge on the sphere, and CB be the capacitance of the sphere. Since the two spheres are connected with a wire, their potential (V) will become equal.
Let EAbe the electric field of sphere A and EB be the electric field of sphere B. Therefore, their ratio,
However 
And 
Putting the value of (2) in (1), we obtain
Therefore, the ratio of electric fields at the surface is
.
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