Question

Two small spherical insulators separated by 2.5 cm, which is much greater than either of their diameters. Both carry positive charge, one +60.0 microCoulombs and the other +6.66 microCoulombs. A third positive charge remains at rest between the two spheres and along the line joining them. What is the position of this charged sphere?

Answer 1

Answer:

1.875 cm from 60 microcoulomb charge.

Explanation:

Let the third charge be Q. Let it be put at x distance from 60 micro coulomb charge for balance.

Force on this charge due to first charge

= $\frac{k\times60\times10^{-6}Q}{x^2}$

Force on this charge due to second charge

= $\frac{k\times6.66\times10^{-6}Q}{(2.5-x)^2}$

Since both these forces are equal $\frac{k\times60\times10^{-6}Q}{x^2}=\frac{k\times6.66\times10^{-6}Q}{(2.5-x)^2}$

$\frac{60}{6.66} = \frac{x^2}{(2.5-x)^2}$$\frac{x}{2.5 -x} = \frac{3}{1}$

x = 1.875

1.875 cm from 60 microcoulomb charge.