Question

Two charged spheres 10 cm apart attract each other with a force of 3.0 x 10⁻⁶ N. What force results from an uncharged, identical sphere is touched to one of the spheres, and then taken far away. ?

Answer 1

Given data:

* The distance between the charged spheres is d = 10 cm.

* The electrostatic force between the charged spheres is,

`F=3*10^(-6)\text{ N}`

Solution:

The electrostatic force between the charged spheres is,

`F=(kq_1q_2)/(d^2)`

where k is the electrostatic force constant,

When the uncharged identical sphere is touched with the charged sphere, then half the charge from the charged sphere is transferred to the uncharged sphere. Thus, the remaining charge on the charged sphere is,

`q_1^(\prime)=(q_1)/(2)`

Thus, the electrostatic force between the charged spheres becomes,

`\begin{gathered} F^(\prime)=(kq_1^(\prime)q_2)/(d^2) \\ F^(\prime)=\frac{_{}kq_1q_2}{2d^2} \end{gathered}`

The uncharged sphere after charging with half charge is taken far away thus it does not exert the electrostatic force on the two charged spheres present 10 cm apart.

Substituting the known values,

`\begin{gathered} F^(\prime)=(F)/(2) \\ F^(\prime)=(3*10^(-6))/(2) \\ F^(\prime)=1.5*10^(-6)\text{ N} \end{gathered}`

Thus, the electrostatic force between the charged spheres is,

`1.5*10^(-6)\text{ N}`