Electric Charge, Force, and Electric Field

Electric Charge and Coulomb's Law

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric or magnetic field. Coulomb's Law describes the force between two point charges.

• Coulomb's Law: The magnitude of the electric force between two point charges is given by:

• Electric Field (E): The electric field produced by a point charge at a distance r is:

• Electric Potential Energy (Ue): The potential energy between two charges:

• Electric Potential (V): The potential at a distance r from a point charge:

• Force from Electric Field: The force on a charge in an electric field:

• Potential Difference: The change in electric potential between two points:

• Constants:

  • (Coulomb's constant)

  • (elementary charge)

  • (electron mass)

Example:

Calculate the force between two electrons separated by 1 nm:

Current, Capacitors, Resistors, and DC Circuits

Capacitance and Capacitors

Capacitors store electric charge and energy. Capacitance depends on geometry and material.

• Charge Stored:

• Parallel Plate Capacitance:

• Permittivity of Free Space:

• Energy Stored:

Resistors and Ohm's Law

Resistors impede current flow. Ohm's Law relates voltage, current, and resistance.

• Ohm's Law:

• Resistance:

• Temperature Dependence:

Power in Circuits

• Power:

Series and Parallel Combinations

• Resistors in Series:

• Resistors in Parallel:

• Capacitors in Series:

• Capacitors in Parallel:

Charging and Discharging Capacitors

• Charging:

• Discharging:

Example:

Find the equivalent resistance of three resistors (2 Ω, 4 Ω, 6 Ω) in parallel:

Magnetic Force and Magnetic Fields

Magnetic Force

Charged particles and currents experience forces in magnetic fields.

• Force on a Current-Carrying Wire:

• Force on a Moving Charge:

Magnetic Field Strength

• Field from a Long Straight Wire:

• Field in a Solenoid:

• Permeability of Free Space:

Magnetic Field Calculations

• Ampère's Law:

• Force Between Parallel Wires:

Example:

Calculate the magnetic field 2 cm from a wire carrying 5 A:

Vectors and Trigonometry

Vector Components and Magnitude

Vectors are quantities with both magnitude and direction. Trigonometry is used to resolve vectors into components.

• Sine:

• Cosine:

• Tangent:

• Magnitude of a Vector:

• Direction of a Vector:

Example:

A vector has components , . Find its magnitude and direction:

Summary Table: Key Constants and Formulas

Additional info: Academic context and explanations have been added to make the formula sheet self-contained and suitable for exam preparation.