Answer:
The magnitude of the force if the size of each charge is doubled and the distance between the spheres is doubled is 64 newtons.
Explanation:
The magnitude of electrostatic force between two charged objects is:
[tex]F_{e}=k\frac{\mid q_{1}q_{2}\mid}{r^{2}} [/tex]
With [tex]q_{1} [/tex]and [tex]q_{2} [/tex] 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:
[tex]64N=k\frac{\mid q_{1}q_{2}\mid}{r^{2}} [/tex] (1)
Now if each charge is doubled and the distance between them is doubled too:
[tex]F'_{e}=k\frac{\mid 2q_{1}2q_{2}\mid}{(2r)^{2}} [/tex]
[tex] F'_{e}=k\frac{4\mid q_{1}q_{2}\mid}{4r^{2}} [/tex]
[tex]F'_{e}=k\frac{\mid q_{1}q_{2}\mid}{r^{2}} [/tex], Note that it's the same on the right side equation (1) so [tex]F'_{e} = 64N [/tex]
Magnitude of the force is the same!
