Chapter 21: Electric Charge and Electric Field

21.1 Properties of Electric Charges

Electric charge is a fundamental property of matter that gives rise to electric forces and interactions. There are two types of electric charges: positive and negative. Like charges repel each other, while opposite charges attract. The study of how charges interact is called electrostatics.

• Charge Conservation: The total electric charge in an isolated system remains constant. Charge can be transferred but not created or destroyed.

• Quantization of Charge: Electric charge exists in discrete packets, with the elementary charge C being the smallest unit observed in isolation.

• Structure of Matter: Atoms consist of a positively charged nucleus (protons and neutrons) surrounded by negatively charged electrons. The electric attraction between protons and electrons holds the atom together.

• Ions: Atoms can gain or lose electrons, becoming ions. A positive ion (cation) has lost electrons, while a negative ion (anion) has gained electrons.

21.2 Charging Objects: Contact and Induction

Objects can be charged by transferring electrons through contact or by rearranging charges via induction.

• Charging by Contact: When two objects touch, electrons can move from one to the other, resulting in one object becoming positively charged and the other negatively charged.

• Charging by Induction: A charged object brought near a conductor can cause a redistribution of charges within the conductor, even without direct contact. If the conductor is grounded, electrons can enter or leave, resulting in a net charge.

• Polarization: In insulators, charges cannot move freely, but the charge distribution can shift slightly, causing polarization. This allows charged objects to attract neutral insulators.

21.3 Conductors, Insulators, and Semiconductors

Materials are classified based on their ability to allow electric charge to move:

• Conductors: Materials (like metals) that allow free movement of charge due to the presence of free electrons.

• Insulators: Materials (like glass or rubber) in which charges do not move freely.

• Semiconductors: Materials with electrical properties intermediate between conductors and insulators.

21.4 Conservation and Quantization of Charge

The principle of charge conservation states that the algebraic sum of all electric charges in any closed system is constant. All observable charge is quantized in units of the elementary charge .

• Example: Rubbing a balloon on hair transfers electrons, making the balloon negatively charged and the hair positively charged. The total charge remains constant.

21.5 Applications: Electrostatic Painting

Electrostatic principles are used in industrial applications such as painting. Negatively charged paint droplets are attracted to a positively charged or grounded metal object, ensuring efficient and uniform coating.

21.6 Point Charges and Continuous Charge Distributions

A point charge is an idealized model of a particle with charge but negligible size. In reality, charges can be distributed over a length, surface, or volume, forming a continuous charge distribution.

• Point Charge: Used when the size of the charged object is much smaller than the distance between charges.

• Continuous Distribution: Used when charges are spread out over an object.

21.7 Coulomb’s Law

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

• Mathematical Form:

where is Coulomb’s constant, and are the charges, and is the distance between them.

• Direction: The force acts along the line joining the two charges. Like charges repel; unlike charges attract.

21.8 Measuring Electric Forces

Coulomb measured electric forces using a torsion balance, which detects the tiny forces between charged objects.

21.9 Comparison: Electric vs. Gravitational Forces

Both electric and gravitational forces are inverse-square laws, but electric forces are vastly stronger at the atomic scale.

• Gravitational Force:

• Electric Force:

• For two protons, the electric repulsion is about times stronger than the gravitational attraction.

21.10 Superposition Principle

The superposition principle states that the net force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge separately.

• Formula:

• Forces must be added as vectors, not just algebraically.

21.11 Worked Examples: Forces Between Charges

Examples illustrate how to apply Coulomb’s law and the superposition principle to calculate forces in one and two dimensions.

• Example 1: Two charges nC and nC separated by cm. Find the force each exerts on the other.

• Example 2: Three charges on a line. Calculate the net force on one charge using vector addition.

• Example 3: Three charges in a plane. Use symmetry and vector components to find the net force.

• Example 4: Three charges at the corners of a right triangle. Find the resultant force on one charge.

Summary Table: Key Properties of Electric Charge

Additional info:

• Polarity of water molecules is important for their role as a solvent, due to the uneven distribution of charge within the molecule.

• Electrostatic phenomena are foundational for understanding electric fields, which will be covered in subsequent sections.