Lesson: Chapter - 13

Electric Force

There is a certain force associated with electric charge, so when a net charge is produced, a net electric force is also produced. We find electric force at work in anything that runs on batteries or uses a plug, but that isn’t all. Almost all the forces we examine in this book come from electric charges. When two objects “touch” one another—be it in a car crash or a handshake—the atoms of the two objects never actually come into contact. Rather, the atoms in the two objects repel each other by means of an electric force.

Coulomb’s Law

Electric force is analogous to gravitational force: the attraction or repulsion between two particles is directly proportional to the charge of the two particles and inversely proportional to the square of the distance between them. This relation is expressed mathematically as Coulomb’s Law:

Video Lesson - Coulombs Law

In this equation, q₁ and q₂ are the charges of the two particles, r is the distance between them, and k is a constant of proportionality. In a vacuum, this constant is Coulumb’s constant, k_o, which is approximately 9 × 10⁹ N · m² / C². Coulomb’s constant is often expressed in terms of a more fundamental constant—the permittivity of free space, e_o, which has a value of 8.85 × 10^-12 C²/ N · m²:

If they come up on Physics, the values for k_o and e_o will be given to you, as will any other values for k when the electric force is acting in some other medium.

Example

According to Coulomb’s Law, the electric force between the two particles is initially

If we double one of the charges and double the value of r, we find:

Doubling the charge on one of the particles doubles the electric force, but doubling the distance between the particles divides the force by four, so in all, the electric force is half as strong as before.

Superposition

If you’ve got the hang of vectors, then you shouldn’t have too much trouble with the law of superposition of electric forces. The net force acting on a charged particle is the vector sum of all the forces acting on it. For instance, suppose we have a number of charged particles, q₁, q₂, and q₃. The net force acting on q₁ is the force exerted on it by q₂ added to the force exerted on it by q₃. More generally, in a system of n particles:

where is the force exerted on particle 1 by particle n and F₁ is the net force acting on particle 1. The particle in the center of the triangle in the diagram below has no net force acting upon it, because the forces exerted by the three other particles cancel each other out.

Example

In the figure above, what is the direction of the force acting on particle A?

The net force acting on A is the vector sum of the force of B acting on A and the force of C acting on A. Because they are both positive charges, the force between A and B is repulsive, and the force of B on A will act to push A toward the left of the page. C will have an attractive force on A and will pull it toward the bottom of the page. If we add the effects of these two forces together, we find that the net force acting on A is diagonally down and to the left.

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