Question

Two charged conducting spheres are connected to each other by a wire. find the ratio of electric fiekd at the surfaces of the two spheres

Answer 1

Let a be the radius of a sphere A , QA be the charge on the sphere, and C A be the capacitance of the sphere.
Let b be the radius of a sphere B , QB be the charge on the sphere, and C B be the capacitance of the sphere. Since the two spheres are connected with a wire, their potential (V) will become equal.
Let E A be the electric field of sphere A and $E_B4 be the electric field of sphere B. Therefore, their ratio,
E A
E B = Q4
4 π ∈ 0 × a 2 × b2 ×4 π ∈ 0
Q 8
E A
E B = Q A
Q B × b 2
a 2 ------------(1)
How ever QA
QB = C 1V
C B V
and C A
C B = a
b ----------------(2)
Putting the value of (2) in (1), we obtain
E A
E B = a
b b2
a 2 = a
b
Therefore, the ratio of electric fields at the surface is b
a