Let a be the radius of a sphere A, QAbe 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 EA be the electric field of sphere A and EB be the electric field of sphere B. Therefore, their ratio,
EAEB=QA4π∈0×a2×b2×4π∈0QB
EAEB=QAQB×b2a2 ...(1)
However, QAQB=CAVCBV
And CACB=ab
∴QAQB=ab ...(2)
Putting the value of (2) in (1), we obtain
∴EAEB=abb2a2=ba
Therefore, the ratio of electric fields at the surface is ba.
A sharp and pointed end can be treated as a sphere of very small radius and a flat portion behaves as a sphere of much larger radius.Therefore, charge density on sharp and pointed ends of the conductor is much higher than on its flatter portions.