Chapter 5: Electric Force and Coulomb’s Law

Introduction to Electric Force

Electric force is a fundamental interaction between charged particles, described quantitatively by Coulomb’s Law. This force is responsible for many phenomena in physics, including the behavior of insulators and conductors, and is essential for understanding electrostatics.

• Electric Force: The force exerted by one charged object on another due to their electric charges.

• Electrostatics: The study of stationary electric charges and the forces between them.

• Newton’s Third Law: For every action, there is an equal and opposite reaction. In the context of electric force, the force exerted by charge q1 on q2 is equal in magnitude and opposite in direction to the force exerted by q2 on q1.

Polarization of Insulators

When a charged object is brought near a neutral insulator, the charges within the molecules of the insulator can shift slightly. This process is called polarization, and it leads to an attractive force between the charged object and the neutral insulator.

• Polarization: Redistribution of charges within molecules of an insulator when exposed to an external electric field.

• Attraction of Neutral Objects: Both positive and negative charges can attract neutral insulators due to induced polarization.

• Example: A negatively charged comb can pick up small pieces of neutral paper or plastic due to polarization-induced attraction.

Additional info: The net force is attractive because the induced positive charges in the insulator are closer to the charged object than the induced negative charges, resulting in a stronger attractive force.

Coulomb’s Law

Coulomb’s Law quantifies the electric force between two point charges. The magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Point Charges: Idealized charges located at a single point in space.

• Coulomb’s Law (Vector Form):

• Coulomb’s Law (Magnitude):

• Variables:

  • F: Magnitude of the electric force

  • q1, q2: Magnitudes of the point charges

  • r: Distance between the charges

  • k: Coulomb’s constant ( N·m2/C2)

• Direction: The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

• Comparison with Newton’s Law of Gravitation: Both laws have an inverse-square dependence on distance, but electric forces can be both attractive and repulsive, while gravitational forces are always attractive.

Fundamental Electric Constants

Several constants are essential for calculations involving electric force:

Additional info: Coulomb’s constant can also be expressed as .

Principle of Superposition

The principle of superposition states that when multiple charges are present, the total electric force on any one charge is the vector sum of the forces exerted by all other charges individually.

• Superposition Principle: Forces from multiple charges add vectorially.

• Application: Used to calculate net force in systems with more than two charges.

• Example: If three charges are present, the net force on one charge is the sum of the forces from the other two.

Comparison: Electric vs. Gravitational Force

Both electric and gravitational forces follow an inverse-square law, but differ in their nature and magnitude.

Additional info: The gravitational constant is N·m2/kg2.