A conducting sphere is charged. If the electric field at a distance 20 cm from the centre of the sphere is 1.2 × 10³ NC^-1 and points radially inwards, the net charge on the sphere is:

Concept:

We know that for a conducting sphere, the electric field outside the sphere is the same as the field due to a point charge located at the center of the sphere. So, we can use the formula for the electric field due to a point charge to find the net charge on the sphere.

The electric field due to a point charge q at a distance r from it is given by:

E = k× q/r²

where k is the Coulomb constant.

In this case, the electric field at a distance of 20 cm from the center of the sphere is given as 1.2 × 10³ NC^-1, and it points radially inwards.

This means that the point charge at the center of the sphere is negative.

So, we have:

E = k×q/r²

= q = \(\frac{Er^2}{k}\)------(1)

Calculation:

Given that 

E = 1.2 × 103 NC-1 

r = 20 cm = 0.2 m.

k = 4.5 × 109

Substituting values of k, r, E in the equation we get,

q = \(\frac{Er^2}{k}\)

= \(\frac{1.2×10^3×0.04}{9×10^9}\)

= 5.33 ×10-9 C

Since the point charge at the center of the sphere is negative.

q = - 5.3 ×10-9 C 

The correct answer is option (4)