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

one fourth

Step-by-step explanation:

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 (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)=(1)/(1^2)=1`

while the force between p and S is

`E_(pS)=(1)/(4^2)=(1)/(16)`

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