Chapter 16: Electric Charge and Electric Field

16.1 Static Electricity; Electric Charge and Its Conservation

Static electricity arises from the transfer of electric charge between objects, typically by rubbing. The concept of electric charge dates back to ancient Greece, where amber, when rubbed with fur, could attract small objects. The Greek word for amber is elektron, the root of the word 'electricity'.

• Electric Charge: A fundamental property of matter that comes in two types: positive and negative. Like charges repel; opposite charges attract.

• Conservation of Charge: The total electric charge in an isolated system remains constant. The arithmetic sum of all charges does not change in any interaction.

• Charging by Rubbing: Rubbing transfers electrons from one object to another, causing one to become negatively charged and the other positively charged.

• Example: Rubbing a plastic ruler with a cloth transfers electrons, charging the ruler.

16.2 Electric Charge in the Atom

Atoms are composed of a small, positively charged nucleus surrounded by a cloud of negatively charged electrons. Atoms are electrically neutral when the number of protons equals the number of electrons.

• Nucleus: Small, massive, and positively charged (contains protons and neutrons).

• Electron Cloud: Large, low-density region containing negatively charged electrons.

• Polar Molecules: Molecules that are neutral overall but have uneven charge distribution (e.g., water molecule).

• Example: Rubbing can move electrons from one object to another, charging them.

16.3 Insulators and Conductors

Materials can be classified based on their ability to conduct electric charge.

• Conductors: Materials (like metals) where charge flows freely.

• Insulators: Materials (like wood, glass) where charge does not flow freely.

• Semiconductors: Materials with conductivity between conductors and insulators.

16.4 Induced Charge; the Electroscope

Objects can be charged by conduction (direct contact) or induction (without contact). The electroscope is a device used to detect electric charge.

• Charging by Conduction: Direct transfer of electrons by contact with a charged object.

• Charging by Induction: Redistribution of charges within an object due to the presence of a nearby charged object, without direct contact.

• Nonconductors: Do not become charged by conduction or induction but can experience charge separation.

• Electroscope: Device with metal leaves that spread apart when charged, used to detect and determine the sign of electric charge.

16.5 Coulomb's Law

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

• Coulomb's Law:

• Unit of Charge: Coulomb (C)

• Proportionality Constant:

• Charge on Electron:

• Permittivity of Free Space:

• Superposition Principle: The net force on a charge is the vector sum of the forces from all other charges.

16.6 Solving Problems Involving Coulomb's Law and Vectors

To solve problems involving multiple charges, use vector addition to find the net force.

• Net Force:

• Vector Addition: Forces are added using the tail-to-tip method or by resolving into components.

16.7 The Electric Field

The electric field describes the force per unit charge at a point in space. It is a vector field, with both magnitude and direction.

• Definition:

• For a Point Charge: or

• Force on a Charge:

• Superposition Principle:

• Problem Solving Steps:

  1. Draw a diagram showing all charges and fields.

  2. Calculate forces using Coulomb's law.

  3. Add forces vectorially.

16.8 Field Lines

Electric field lines visually represent the direction and strength of the electric field.

• Field Line Properties:

  • Start on positive charges, end on negative charges.

  • The number of lines is proportional to the magnitude of the charge.

  • The field is stronger where lines are closer together.

  • The field is tangent to the field line at any point.

• Electric Dipole: Two equal and opposite charges; field lines emerge from the positive and terminate on the negative charge.

• Parallel Plates: The electric field between two closely spaced, oppositely charged plates is uniform (constant in magnitude and direction).

16.9 Electric Fields and Conductors

Conductors in electrostatic equilibrium have unique properties regarding electric fields and charge distribution.

• Static Electric Field: Zero inside a conductor; if not, charges would move.

• Surface Charge: Net charge resides on the surface of a conductor.

• Field Direction: The electric field at the surface is perpendicular to the surface.

16.10 Gauss’s Law

Gauss’s law relates the electric flux through a closed surface to the charge enclosed by that surface. It is especially useful for problems with high symmetry.

• Electric Flux:

• Flux through a Closed Surface:

• Gauss’s Law:

• Application: Used to find electric fields in situations with symmetry (spherical, cylindrical, planar).

16.11 Electric Forces in Molecular Biology: DNA Structure and Replication

Electrostatic forces play a crucial role in molecular biology, particularly in the structure and replication of DNA.

• DNA Structure: Double helix composed of nucleotide bases (A, T, G, C).

• Base Pairing: A-T and G-C pairs attract each other through electrostatic forces (hydrogen bonds).

• Replication: During cell replication, complementary bases are attracted by these forces, ensuring accurate copying of genetic information.

16.12 Photocopy Machines and Computer Printers Use Electrostatics

Electrostatics is used in photocopy machines and laser printers to transfer images onto paper.

• Photocopy Machine:

  • Drum is charged positively.

  • Image is focused on the drum; only black areas retain charge and attract toner.

  • Toner is transferred to paper and sealed by heat.

• Laser Printer: Similar process, but a computer controls the laser to form the image on the drum.

Summary Table: Key Concepts in Chapter 16