Question

Charge q is 1 unit of distance away from the source charge S. Charge p is four times further away. The force exerted between S and q is _____ the force exerted between S and p.
one0fourth
four times
one0sixteenth
sixteen times

Answer 1

The correct answer for the question that is being presented above is this one: "one0fourth." Charge q is 1 unit of distance away from the source charge S. Charge p is four times further away. The force exerted between S and q is one0fourth the force

Answer 2

The correct answer is:

sixteen times

In fact, the distance between charge q and the source S is 1 unit. Instead, the distance between charge p and the source S is 4 units. The magnitude of the electrostatic force is inversely proportional to the square of the distance between the charge and the source:

$E \sim \frac{1}{r^2}$

where r is the distance. If we take the force between q and S as reference, we have r=1, so that

$E_{qS}=\frac{1}{1^2}=1$

while the force between p and S is

$E_{pS}=\frac{1}{4^2}=\frac{1}{16}$

Therefore, we see that the force exerted between q and S is 16 times the force exerted between p and S.