A 8.01-nC charge is located 1.95 m from a 4.06-nC point charge.

(a) Find the magnitude of the electrostatic force that one charge exerts on the other.
(b) Is the force attractive or repulsive?

Coulomb’s Law

F = k •q1•q2/r²,
k =9•10^9 N•m^2/C^2
q1 = 8,01•10^-9 C,
q2 = 4.06•10^-9 C,
r =1.96 m
repulsive force

To find the electrostatic force between two charges, we can use the formula:

\[ F = \frac{{k \cdot |q_1 \cdot q_2|}}{{r^2}} \]

where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant (k = 8.99 × 10^9 N m^2/C^2)
- q1 and q2 are the charges of the two particles
- r is the distance between the two charges

Let's calculate the magnitude of the electrostatic force:

a) Plugging in the given values:
q1 = 8.01 nC = 8.01 × 10^(-9) C
q2 = 4.06 nC = 4.06 × 10^(-9) C
r = 1.95 m

F = (8.99 × 10^9 N m^2/C^2) * |8.01 × 10^(-9) C * 4.06 × 10^(-9) C| / (1.95 m)^2

Calculating the expression:

F ≈ (8.99 × 10^9 N m^2/C^2) * (8.01 × 10^(-9) C * 4.06 × 10^(-9) C) / (1.95^2 m^2)
F ≈ 7.99 × 10^(-3) N

Therefore, the magnitude of the electrostatic force is approximately 7.99 × 10^(-3) N.

b) To determine if the force is attractive or repulsive, we need to look at the signs of the charges. The given charges are positive, which means they have the same sign.

Since both charges are positive, the electrostatic force will be repulsive.

To find the magnitude of the electrostatic force between two charges, we can use Coulomb's Law, which states that the force, F, is equal to the product of the charges (q₁ and q₂) divided by the square of the distance (r) between them, multiplied by a constant, k, known as the electrostatic constant.

(a) So, to find the magnitude of the electrostatic force:

F = (k * |q₁ * q₂|) / r²

Where:
- |q₁| and |q₂| are the magnitudes of the charges, and they can be written as positive values since the magnitude does not change the nature of the force.
- r² is the square of the distance between the charges.

The electrostatic constant, k, is approximately equal to 8.99 * 10^9 N·m²/C².

Let's plug in the given values into the formula:

q₁ = 8.01 nC = 8.01 * 10^(-9) C
q₂ = 4.06 nC = 4.06 * 10^(-9) C
r = 1.95 m

F = (8.99 * 10^9 N·m²/C² * |8.01 * 10^(-9) C * 4.06 * 10^(-9) C|) / (1.95 m)²

Now we can solve for the magnitude of the electrostatic force using a calculator:

F ≈ 8.2908 * 10^(-2) N

Thus, the magnitude of the electrostatic force that one charge exerts on the other is approximately 8.2908 * 10^(-2) N.

(b) To determine if the force is attractive or repulsive, we need to consider the signs of the charges.
- If the charges have the same sign (both positive or both negative), the electrostatic force is repulsive.
- If the charges have opposite signs (one positive and one negative), the electrostatic force is attractive.

In this case, one charge is positive and the other is also positive, so the force is repulsive.