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Coulomb’s Law

Coulomb’s Law

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Coulomb's Law is a concept discovered by Charles-Augustin de Coulomb through experiments. It shows that electric charges can affect each other regardless of the mass of the objects. To learn more about this force, we need to study Coulomb's Law.

Coulomb’s law definition and equation

Coulomb's Law is a fundamental principle of physics which states that electrically charged objects in close proximity will exert a force on each other. This force is directly proportional to the net charge of the objects and inversely proportional to the square of the distance between them. Mathematically, Coulomb's Law is expressed through the equation F=k(q1q2/r^2), where F is the force in Newtons, q1 and q2 are the charges in Coulombs, r is the distance in meters, and k is Coulomb's constant with a value of 8.99 x 10^9 N·m2/C2. The electrostatic force is a vector quantity measured in Newtons.

Coulomb’s law: electrostatic force between two charges

When two electric charges interact, there are actually two forces involved. One is the force that the first charge exerts on the second charge, represented by F12. The other is the force that the second charge exerts on the first charge, represented by F21. Like charges repel each other, while unlike charges attract. This is known as the electrostatic force in physics. Check out the image below for a visual representation of these forces.

Like charges repel (above) and unlike charges attract each other (below)

The electrostatic force between the electron and proton in a hydrogen atom is calculated using Coulomb's law. The equation for this is F = 4πε0r2q1q2, where F is the force, ε0 is the permittivity of free space, r is the distance between the two charges, and q1 and q2 are the charges of the electron and proton respectively. Using the given information, the force between the electron and proton is calculated to be 8.98 x 10-8 N.

Coulomb’s law: electrostatic force between multiple charges

To find the net electrostatic force exerted on the test charge Q, we need to first calculate the individual forces exerted on Q by q1 and q2 using Coulomb's law. The equation for this is F = kq1q2/r^2, where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

First, let's calculate the force exerted on Q by q1. Using the given values, we get:

F1 = kq1Q/d^2 = (9 x 10^9 Nm^2/C^2) x (2e) x (-3e) / (3.0 x 10^-8 m)^2 = -12 N

The negative sign indicates that the force is attractive, since q1 and Q have opposite charges.

Next, let's calculate the force exerted on Q by q2:

F2 = kq2Q/d^2 = (9 x 10^9 Nm^2/C^2) x (-4e) x (-3e) / (3.0 x 10^-8 m)^2 = 24 N

The positive sign indicates that the force is repulsive, since q2 and Q have the same charge.

Now, we can find the net force on Q by adding the individual forces as vectors:

Fnet = F1 + F2 = -12 N + 24 N = 12 N

Therefore, the net electrostatic force exerted on the test charge Q is 12 N.

Diagram showing three point-like particles exerting electrostatic forces on each other
Diagram showing three point-like particles exerting electrostatic forces on each other

Coulomb’s law states that two or more electrically charged objects will exert a force on each other when they are close enough. The magnitude of this force is proportional to the net charge of the particles and inversely proportional to the square of the distance between the particles. This force is known as the electrostatic force, and like charges repel and unlike charges attract each other.

To calculate the Coulomb's law forces between multiple charges, we use the principle of superposition This means that we take two forces at a time and calculate their electrostatic forces. We then add all the forces together (as vectors) to find the resultant force. For example, in the given question, we have two source charges (q1 and q3), a test charge (q2), distances (r21 and r23), and we are asked to find a force. This calls for Coulomb’s law and superposition of forces. There are two forces: F→ = F→21 + F→23 = 1/4πε0 [q2q1r21^2j^ + (−q2q3r23^2i^)].

Coulomb’s Law

What is Coulomb’s law?

Coulomb’s law is a law of physics that states when two or more electrically charged objects are close enough to each other, they exert a force on each other. The magnitude of this force is proportional to the net charge of the particles and inversely proportional to the square of the distance between the particles under study.

How do you find q1 and q2 in Coulomb’s law?

You can find q1 and q2 in Coulomb’s law by using the equation: F = k . (q1.q2/r2) where F is the magnitude of the force between the charges, q1 and q2 are the charges measured in Coulombs, r is the distance between the charges measured in metres, and k is Coulomb's constant with a value of 8.99 ⋅ 109 Nm2/C2.

Why is Coulomb’s law valid for point charges?

Coulomb’s law is only valid for point-like charges. This is due to the fact that when the two charged bodies are put together, the charge distribution does not remain uniform.

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