A charged particle A exerts a force of 2.39 ìN to the right on charged particle B when the particles are 13.3 mm apart. Particle B moves straight away from A to make the distance between them 16.1 mm. What vector force does particle B then exert on A?

To find the force vector that particle B exerts on particle A, we will make use of Coulomb's law and vector addition.

Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

1. First, let's calculate the charge of particle B. Unfortunately, the charge is not given in the problem statement. We'll need to assume a charge value for particle B.

2. Suppose we assume the charge of particle B to be qB. Since the problem does not specify the charges of the particles, we won't be able to determine the value of qB.

3. The force exerted by particle A on particle B is given as 2.39 μN to the right. This means it is a force vector pointing to the right.

4. We also know that the distance between the particles when this force is exerted is 13.3 mm. This gives us the magnitude of force FA on particle B.

5. Using Coulomb's law, we can calculate the magnitude of the force FA using the formula:

FA = k * (|qA| * |qB|) / r²

Where:
FA is the magnitude of the force between A and B
k is the electrostatic constant (k ≈ 9 x 10^9 N.m²/C²)
|qA| and |qB| are the absolute values of the charges of particle A and B
r is the distance between the particles

6. Rearranging the formula, we can solve for |qB|:

|qB| = (FA * r²) / (k * |qA|)

Substituting the given values, we can find |qB|.

7. After obtaining the value of |qB|, we need to find the force vector that particle B exerts on particle A when the distance between them is 16.1 mm.

8. Using Coulomb's law again, we can calculate the magnitude of the force FB using the formula:

FB = k * (|qA| * |qB|) / r²

Where:
FB is the magnitude of the force between A and B (when they are 16.1 mm apart)
k is the electrostatic constant
|qA| and |qB| are the absolute values of the charges of particle A and B
r is the distance between the particles (16.1 mm)

9. We now have the magnitude of the force FB between particle A and particle B. To determine the direction of the force, we need to analyze the relative charges of the particles. If particle B has a positive charge, the force vector should point away from B, in the opposite direction of particle B's motion. If particle B has a negative charge, the force vector should point towards B, in the direction of particle B's motion.

10. Finally, we represent the force vector FB using appropriate notation, considering both magnitude and direction.

I am not going to lay out how to do all of these for you. Try yourself.