Tru Physics

Chapter 1: Electric Charge and Coulomb’s Law

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1.1 Introduction to Electric Charge

Electric charge is a fundamental property of matter. There are two types of electric charge: positive and negative. Objects with like charges repel each other, while objects with opposite charges attract each other. The fundamental unit of charge is the elementary charge (e), which is the charge of a proton (positive) or an electron (negative). The elementary charge has a magnitude of approximately 1.602 \times 10^{-19} \text{ Coulombs (C).}

1.2 Coulomb’s Law

Coulomb’s Law describes the force between two charged objects. The formula for Coulomb’s Law is as follows:

F = k \dfrac{|q_1 q_2|}{r^2} = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{|q_1 q_2|}{r^2}

where F is the magnitude of the electrostatic force between the objects, q_1 and q_2 are the magnitudes of the charges, r is the distance between the charges, and k is the electrostatic constant, approximately 8.99 \times 10^9 \frac{\text{ N} \cdot \text{m}^2}{\text{C}^2}.

As you can see from the equation above:

k = \dfrac{1}{4 \pi \varepsilon_0}

where \varepsilon_0 is the vacuum permittivity constant, equal to about 8.854 \times 10^{-12} \text{ F/m.}

1.3 Properties of Coulomb’s Law

  • Coulomb’s Law is an inverse-square law. This means that the force between two charges decreases with the square of the distance between them.
  • The direction of the force depends on the signs of the charges involved. If the charges are of opposite signs, the force is attractive, and if they are of the same sign, the force is repulsive.
  • The force acts along the line connecting the two charges.

1.4 Superposition Principle

When dealing with multiple charges, the superposition principle applies. It states that the net force on a charge is the vector sum of the individual forces exerted on it by each of the other charges in the system. The principle holds because the electrostatic force is a conservative force.

1.5 Conductors and Insulators

In the context of electric charge, materials can be classified as conductors or insulators. Conductors, like metals, allow charges to move freely within them, whereas insulators, like glass or plastic, inhibit the movement of charges. In conductors, the movement of charges results in the redistribution of charge on the surface until the net force on each charge is zero.

1.6 Charging by Conduction and Induction

Charging by conduction involves direct contact between two objects, causing a transfer of charge until both objects have the same potential. Charging by induction, on the other hand, involves bringing a charged object close to a neutral object without direct contact. This process creates a separation of charges in the neutral object, with one side becoming positively charged and the other side negatively charged.

Chapter Summary

In this chapter, we have covered the basic concepts of electric charge and Coulomb’s Law, which describes the force between charged objects. We have also discussed the superposition principle, conductors and insulators, and methods of charging objects. These foundational concepts will be essential for understanding more advanced topics in electricity and magnetism throughout this course.

Continue to Chapter 2: Electric Fields

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