Given two metal balls (that are identical) with charges LaTeX: q_1q 1and LaTeX: q_2q 2. We find a repulsive force one exerts on the other to be LaTeX: 1.35\times10^{-4}N1.35 × 10 − 4 N when they are 20 cm apart. Accidentally, one the the experimenters causes the balls to collide and then repositions them 20 cm apart . Now the repulsive force is found to be LaTeX: 1.406\times10^{-4}N1.406 × 10 − 4 N. What are the initial charges on the two metal balls?

and

Explanation:

According to Coulomb's law, the magnitude of  force between two point object having change and and by a dicstanced is

Where, is the permitivity of free space and

in SI unit.

Before  dcollision:

Charges on both the sphere are and , d=20cm=0.2m, and N

So, from equation (i)

After dcollision: Each ephere have same charge, as at the time of collision there was contach and due to this charge get redistributed which made the charge density equal for both the sphere t. So, both have equal amount of charhe as both are identical.

Charges on both the sphere are mean of total charge, i.e

d=20cm=0.2m, and N

So, from equation (i)

As given that the force is repulsive, so both the sphere have the same nature of charge, either positive or negative, so, here take the magnitude of the charge.

The equation (ii) become:

From equation (iii)

So, the magnitude of initial charges on both the sphere are Coulombs and Colombs or .

Considerion the nature of charges too,

and