Electric Charge and Its Properties

Nature of Electric Charge

Electric charge is a fundamental property of matter that causes objects to experience a force when placed in an electric or magnetic field. The effects of electric charge are commonly observed as attraction or repulsion between objects.

• Types of Charge: There are two types of electric charge: positive and negative.

• Like charges repel each other, while opposite charges attract.

• Neutral objects can be slightly affected by charged objects due to polarization.

• Discharge/Grounding: The process by which excess charge is removed from an object, making it neutral.

Example: Rubbing a plastic rod with wool transfers electrons from the wool to the rod, making the rod negatively charged. Rubbing a glass rod with silk transfers electrons from the rod to the silk, making the rod positively charged.

Conservation of Charge

The total electric charge in an isolated system remains constant. Electrons can be transferred between objects, but the net charge is conserved.

• SI unit of charge: Coulomb (C)

• Elementary charge: C

Conductors and Insulators

• Conductors: Materials (like metals) in which charges move freely across the surface due to a 'sea of electrons.'

• Insulators: Materials (like plastic or glass) in which charges are localized and do not move freely.

Coulomb's Law

Force Between Point Charges

Coulomb's Law quantifies the electrostatic force between two point charges.

• The magnitude of the force between two point charges and separated by a distance is given by:

• is the electrostatic constant: N·m2/C2

• The direction of the force is along the line joining the charges: repulsive for like charges, attractive for opposite charges.

• For more than two charges, the net force is the vector sum of the individual forces (superposition principle).

Example: If C and C are separated by 0.05 m, the force is:

Electric Field

Definition and Properties

The electric field is a vector field that describes the force per unit charge exerted on a test (probe) charge at any point in space.

• Electric field due to a point charge:

• The direction of is away from positive charges and toward negative charges.

• Field lines indicate the direction and strength of the field; denser lines mean a stronger field.

Superposition of Electric Fields

• The net electric field at a point due to multiple charges is the vector sum of the fields produced by each charge.

Electric Dipoles

An electric dipole consists of two equal and opposite charges separated by a distance.

• Dipole moment: , where is the magnitude of each charge and is the displacement vector from negative to positive charge.

Continuous Charge Distributions

For objects with charge distributed over a length, area, or volume, the electric field is found by integrating over the distribution.

• Linear charge density:

• Surface charge density:

• Volume charge density:

Gauss's Law

Electric Flux and Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface.

• Electric flux:

• Gauss's Law:

• is the permittivity of free space: C2/N·m2

• The law is especially useful for calculating fields of objects with high symmetry (spherical, cylindrical, planar).

Applications of Gauss's Law

• Infinite line of charge: Use a cylindrical Gaussian surface.

• Infinite plane of charge: Use a pillbox Gaussian surface.

• Point charge: Use a spherical Gaussian surface.

Electric Potential and Potential Energy

Electric Potential

Electric potential is the electric potential energy per unit charge at a point in space.

• Potential difference (voltage):

• Relation to electric field:

• Potential due to a point charge:

Electric Potential Energy

• Work done by electric force:

• Change in electric potential energy:

• In a uniform field (such as between parallel plates):

Conservation of Energy

• The total mechanical energy (kinetic + potential) is conserved in the absence of non-conservative forces.

Summary Table: Key Quantities and Formulas

Key Points to Remember

• Electric charge is quantized and conserved.

• Coulomb's Law describes the force between point charges.

• Electric field is a vector; use superposition for multiple sources.

• Gauss's Law is powerful for symmetric charge distributions.

• Electric potential relates to the work done by or against electric fields.

• Energy conservation applies to systems involving electric forces.