Question

Two charged conducting spheres of radii a and b are connected to each other by a wire. Find the ratio of the electric fields at their surfaces.

Answer 1

Let a be the radius of a sphere A, Q_A be the charge on the sphere and C_A be the capacitance of that sphere. Let b be the radius of a sphere B, Q_B be the charge on the sphere, and C_B be the capacitance of that sphere. Since the two spheres are connected by a wire, their potential (V) will become equal. Let E_A be the electric field of sphere A and E_B by the electric field of sphere B. Then,

`E_A/E_B = ((Q_A)/(4piε_0a^2)) xx ((b^2 4piε_0)/(Q_B))`

`E_A/E_B = Q_A/Q_B xx b^2/a^2` ......................(i)

However, `Q_A/Q_B = (C_AV)/(C_BV)` .............(ii)

and `C_A/C_B = a/b` ...........(iii)

Putting the values of (ii) and (iii) in (i), we get,

`E_A/E_B = b/a`

Therefore, the required ratio of electric fields at the surface of the spheres is `b/a`.