Electric Charge and Electric Field

Static Electricity; Electric Charge and Its Conservation

Electric charge is a fundamental property of matter responsible for electric phenomena. Objects can acquire charge through friction, conduction, or induction. There are two types of charge: positive and negative. Like charges repel, and unlike charges attract. The total electric charge in an isolated system is always conserved.

• Conservation of Charge: The algebraic sum of all electric charges in any process remains constant.

• Charging by Friction: Rubbing certain materials together can transfer electrons, resulting in one object becoming negatively charged and the other positively charged.

Electric Charge in the Atom

Atoms consist of a small, positively charged nucleus surrounded by a cloud of negatively charged electrons. The nucleus contains protons (positive) and neutrons (neutral). The overall charge of an atom is neutral unless electrons are added or removed.

• Proton: Positive charge, located in the nucleus.

• Electron: Negative charge, orbits the nucleus.

• Neutron: No charge, located in the nucleus.

• Polar Molecule: A molecule with an uneven distribution of charge, resulting in a dipole moment (e.g., water).

Insulators and Conductors

Materials are classified based on their ability to conduct electric charge:

• Conductors: Materials (e.g., metals) in which electric charge flows freely due to the presence of free electrons.

• Insulators: Materials (e.g., glass, rubber) in which electric charge does not flow freely.

• Semiconductors: Materials with conductivity between conductors and insulators.

Induced Charge; the Electroscope

Charging can occur by conduction (direct contact) or induction (without contact). An electroscope is a device used to detect electric charge.

• Charging by Conduction: Transfer of charge by direct contact.

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

• Electroscope: Device that detects the presence and sign of electric charge.

Coulomb’s Law

Electric Force Between Point Charges

The electric force between two point charges is described by Coulomb’s Law:

• The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

• The force acts along the line joining the charges.

Mathematical Form:

where (Coulomb constant).

• Unit of Charge: Coulomb (C).

• Elementary Charge: C (magnitude of charge on a proton or electron).

• Permittivity of Free Space:

• Coulomb’s law can also be written as:

Examples and Applications

• Forces between multiple charges are found by vector addition of individual forces (superposition principle).

The Electric Field

Definition and Properties

An electric field is a region of space around a charged object where other charges experience a force. The electric field at a point is defined as the force per unit charge:

• Direction of is the direction of the force on a positive test charge.

• For a point charge : or

Electric Field Calculations for Continuous Charge Distributions

For objects with continuous charge distributions, the total electric field is found by integrating the contributions from each infinitesimal charge element:

• Separate integrals are needed for each vector component.

Field Lines

Representation and Interpretation

Electric field lines provide a visual representation of the electric field:

• Lines start on positive charges and end on negative charges.

• The density of lines indicates the strength of the field.

• Field lines never cross.

Electric Fields and Conductors

Properties of Conductors in Electrostatic Equilibrium

• The electric field inside a conductor is zero in electrostatic equilibrium.

• Any excess charge resides on the surface of the conductor.

• The electric field at the surface is perpendicular to the surface.

Motion of a Charged Particle in an Electric Field

The force on a particle of charge in an electric field is . If the mass is known, the acceleration is . The motion can be analyzed using Newton's laws.

Electric Dipoles

Definition and Properties

An electric dipole consists of two equal and opposite charges separated by a distance . The dipole moment is (points from negative to positive charge).

• In a uniform electric field, a dipole experiences a torque but no net force.

• The electric field of a dipole decreases as at distances much greater than .

Summary Table: Key Concepts in Electric Charge and Field

Additional info:

• Some examples and board work are referenced as homework and are not fully detailed here.

• Section on electric forces in molecular biology (DNA) is for self-study and not examinable.