Question

Two identical conducting spheres carry charges Q and 2 Q. When separated by a distance much larger than their diameters, the spheres exert an electrostatic force F on each other. The two spheres are brought into electrical contact and then returned to their original separation. The final electrostatic force between the spheres is________________.

Answer 1

Answer:

Explanation:

Charges are Q and 2Q

distance = d

Force = F

Use coulomb's law

$F = \frac{KQ \times 2Q}{d^{2}}$    

$F = \frac{2KQ^{2}}{d^{2}}$         ... (1)

As they are in contact to each other the charges are shared.

Charge on each sphere, Q' = (Q + 2Q) /2 = 1.5 Q

Let the force is F'

By using Coulomb's law

$F' = \frac{K\times 1.5\times 1.5Q^{2}}{d^{2}}$

$F' = \frac{2.25KQ^{2}}{d^{2}}$     ..... (2)

Divide equation (2) by equation (1)

$\frac{F'}{F} = \frac{2.25}{2}$

F' = 1.125 F