Question

Two conducting spheres are each given a charge Q. The radius of the larger sphere is three times greater than that of the smaller sphere. If the electric field just outside of the smaller sphere is E0, then the electric field just outside of the larger sphere is
3 Two conducting spheres are each given a charge Q.
1/9 Two conducting spheres are each given a charge Q.
9 Two conducting spheres are each given a charge Q.
1/3 Two conducting spheres are each given a charge Q.

Answer 1

Answer:

1/9 of that just outside the smaller sphere

Explanation:

The electric field strength produced by a charged sphere outside the sphere itself is equal to that produced by a single point charge:

$E=k\frac{Q}{r^2}$

where

k is the Coulomb's constant

Q is the charge on the sphere

r is the distance from the centre of the sphere

Calling R the radius of the first sphere, the electric field just outide the surface of the first sphere is

$E_0=k\frac{Q}{R^2}$

The second sphere has a radius which is 3 times that of the smaller sphere:

$R'=3R$

So, the electric field just outside the second sphere is

$E'=k\frac{Q}{R'^2}=k\frac{Q}{(3R)^2}=\frac{1}{9}(k\frac{Q}{R^2})=\frac{E_0}{9}$

So, the correct answer is 1/9.