### Coulomb`s Law in Vector Form Agreement with Newton`s Third Law

Coulomb`s law in vector form is an essential concept in electromagnetism. It describes the interaction between two stationary charged objects and is essential in understanding the behavior of charged particles.

When two charged particles are present, there is an electrostatic force between them. Coulomb`s law can calculate the magnitude of this force. The formula is:

F = (k * Q1 * Q2) / r^2

Where F represents the force between the two particles, k is the Coulomb`s constant, Q1 and Q2 are the charges of the two particles, and r is the distance between them.

However, this law does not just show the magnitude of the force. It also tells us the direction of the force. The force is directed along the line connecting the two particles and is repulsive if the two particles have the same charge and attractive if they have opposite charges.

Now, let`s consider the Newton`s third law of motion, which states that for every action, there is an equal and opposite reaction. This law applies to the relationship between charged particles as well.

In other words, if particle A exerts a force on particle B, then particle B must exert an equal and opposite force on particle A. This is a fundamental principle in physics that emphasizes that the forces between charged particles always come in pairs.

When we use Coulomb`s law in vector form, it agrees with Newton`s third law. The vector form of Coulomb`s law is:

F = (Q1 * Q2 / (4πɛr^2)) * r̂

Where r̂ is the unit vector in the direction from Q2 to Q1, and ɛ is the permittivity of space.

The direction of the force vector is given by the unit vector r̂. Moreover, due to the fact that r̂ is pointing from the source charge to the test charge, this vector indicates the direction of the force exerted on the test charge by the source charge.

Therefore, when we combine Coulomb`s law and Newton`s third law, we see that the force between two charged particles is always pairwise and has equal magnitudes but opposite direction for the charges. This relationship emphasizes that the force between two charged particles is a fundamental feature of electrostatics and plays a vital role in the behavior of charged particles.

In conclusion, Coulomb`s law in vector form is significant in describing the behavior of charged particles. It allows us to determine not only the magnitude but also the direction of the electrostatic force between two charged particles. Furthermore, this law agrees with Newton`s third law and emphasizes that the forces in the interaction between charged particles always exist in a pair with equal magnitudes but opposite directions. This relationship is crucial in understanding the behavior of charged particles in electromagnetism.