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

one-sixteenth

The force exerted between two charges is inversely proportional to the square of the distance between them.

Let's assume the force between S and q is Fq, and the force between S and p is Fp.

The distance between S and q is 1 unit, while the distance between S and p is six times that, which means it is 6 units.

According to the inverse square law, the force is proportional to the inverse square of the distance. Therefore, the force exerted between S and q is (1/1^2) times the force between S and p, and the force exerted between S and p is (1/6^2) times the force between S and q.

Simplifying, we find that Fq = Fp / 1, and Fp = Fq / 36.

Therefore, the force exerted between S and q is equal to the force exerted between S and p.

To find the ratio of the forces exerted between the charges, we need to first understand the relationship between the force and the distance.

The force between two charges is given by Coulomb's Law, which states:

F = (k * q1 * q2) / r^2

Where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.

In this case, we are comparing the forces between charge S and charges q and p.

Let's denote the distance between S and q as r1, and the distance between S and p as r2.

We know that r2 is 6 times greater than r1, which means r2 = 6 * r1.

Now, let's compare the forces:

The force between S and q is given by F1 = (k * q * q) / r1^2. (1)

The force between S and p is given by F2 = (k * q * q) / r2^2. (2)

To find the ratio of the forces, we divide equation (2) by equation (1):

F2 / F1 = (k * q * q) / (r2^2) / ((k * q * q) / (r1^2))
= (k * q * q * r1^2) / (k * q * q * r2^2)
= r1^2 / r2^2

Substituting r2 = 6 * r1, we get:

F2 / F1 = r1^2 / (6 * r1)^2
= r1^2 / (6^2 * r1^2)
= 1 / 6^2
= 1 / 36

Therefore, the force exerted between S and q is 1/36 times the force exerted between S and p.

Use Coulomb's law:

F=Q1*Q2/(4πr²ε0)

Where
Q1, Q2 are magnitudes of point charges
r=distance between Q1 and Q2
ε0 = 8.854*10-12

So we conclude that the forces between point charges are directly proportional to the product of the charges, and inversely proportional to the square of the distance between them.

For example, two charges P1 & P2 placed at 1 cm apart will experience 4 times the force if they had been placed 2 cm apart, assuming there are no other charges in the vicinity.