Question

The electrostatic force between two charged spheres is 64 N. What will the magnitude of the force be if the size of each charge is doubled and the distance between the spheres is doubled?

Answer 1

The magnitude of the force if the size of each charge is doubled and the distance between the spheres is doubled is 64 newtons.

Step-by-step explanation:

The magnitude of electrostatic force between two charged objects is:

`F_(e)=k(\mid q_(1)q_(2)\mid)/(r^(2))`

With
`q_(1)`and
`q_(2)` the charges and r the distance between the charges (in our case the distance between the spheres).At first we have that the force is 64N so:

`64N=k(\mid q_(1)q_(2)\mid)/(r^(2))` (1)

Now if each charge is doubled and the distance between them is doubled too:

`F'_(e)=k(\mid 2q_(1)2q_(2)\mid)/((2r)^(2))`

`F'_(e)=k(4\mid q_(1)q_(2)\mid)/(4r^(2))`

`F'_(e)=k(\mid q_(1)q_(2)\mid)/(r^(2))`, Note that it's the same on the right side equation (1) so
`F'_(e) = 64N`

Magnitude of the force is the same!