Electrostatics and Electric Charge

• Electrostatics is the study of stationary or slow-moving electric charges

Electric Charge

• Electric charge is a fundamental property of matter causing it to experience force in an electromagnetic field.
• There are two types of electric charge: positive and negative.
• Like charges repel; unlike charges attract.
• The SI unit of electric charge is the coulomb (C).
• Electric charge is quantized, existing in discrete multiples of the elementary charge (e).
• The elementary charge (e) ≈ 1.602 × 10-19 C.
• Charge is conserved, meaning that the total electric charge in an isolated system remains constant.

Coulomb's Law

• Coulomb's Law describes the electrostatic force between two point charges.
• The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Coulomb's Law is expressed as: F = k * |q1 * q2| / r^2
• F is the electrostatic force between the charges.
• q1 and q2 are the magnitudes of the two charges.
• r is the distance between the charges.
• k is Coulomb's constant, k ≈ 8.9875 × 10^9 N⋅m^2/C^2.
• Electrostatic force is a vector quantity, with its direction along the line joining the two charges.

Electric Field

• An electric field is a region of space around an electric charge where another charge experiences a force.
• Electric field intensity (E) is the force per unit positive charge experienced by a test charge placed in the field: E = F/q.
• The SI unit of electric field intensity is newtons per coulomb (N/C) or volts per meter (V/m).
• Electric field lines visualize electric fields.
• Electric field lines point in the direction of the force on a positive test charge.
• The density of field lines indicates the strength of the electric field.
• Electric field due to a point charge: E = k * |q| / r^2.
• The electric field is a vector quantity.

Electric Potential

• Electric potential (V) at a point is the electric potential energy per unit charge.
• Electric potential is a scalar quantity.
• The SI unit of electric potential is the volt (V).
• The electric potential difference between two points is the work done per unit charge to move a charge between those points, V = W/q.
• For a point charge, the electric potential at a distance r is: V = k * q / r.
• Electric potential energy (U) of a charge q at a point where the electric potential is V is: U = q * V.
• Equipotential surfaces are surfaces on which the electric potential is constant.

Capacitance

• Capacitance (C) measures a capacitor's ability to store electric charge.
• Capacitance is the ratio of the charge (Q) stored on a conductor to the potential difference (V) between the conductors: C = Q/V.
• The SI unit of capacitance is the farad (F).
• A capacitor typically consists of two conductors separated by an insulator (dielectric).
• For a parallel-plate capacitor: C = ε0 * A / d.
• ε0 is the permittivity of free space (ε0 ≈ 8.854 × 10-12 F/m).
• A is the area of each plate.
• d is the separation between the plates.

Dielectrics

• A dielectric is an insulating material placed between capacitor plates to increase capacitance.
• The dielectric constant (κ) is the factor by which capacitance increases when a dielectric is inserted, C' = κ * C.
• The electric field within the dielectric is reduced by a factor of κ.
• Dielectric strength is the maximum electric field a dielectric can withstand before breakdown.

Energy Stored in a Capacitor

• A charged capacitor stores electrical potential energy.
• The energy (U) stored in a capacitor is given by: U = (1/2) * C * V^2 = (1/2) * Q * V = (1/2) * Q^2 / C.
• This energy is stored in the electric field between the capacitor plates.

Electric Current

• Electric current (I) is the rate of flow of electric charge through a conductor: I = ΔQ/Δt.
• ΔQ is the amount of charge flowing through a cross-sectional area in a time interval Δt.
• The SI unit of current is the ampere (A), where 1 A = 1 C/s.
• Conventional current is the direction of flow of positive charge, opposite to the flow of electrons.

Resistance and Ohm's Law

• Resistance (R) is the opposition to the electric current flow in a material.
• The SI unit of resistance is the ohm (Ω).
• Ohm's law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it: V = I * R.
• Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it opposes the flow of current.
• Resistance R = ρ * L / A, where L is the length, and A is the cross-sectional area of the conductor.
• Conductivity (σ) is the reciprocal of resistivity (σ = 1/ρ).

Electric Power

• Electric power (P) is the rate at which electrical energy is transferred in a circuit.
• P = V * I = I^2 * R = V^2 / R.
• The SI unit of power is the watt (W).

Series and Parallel Circuits

• Resistors in series: The equivalent resistance is the sum of individual resistances: R_eq = R1 + R2 + R3 + ...
• Current is the same through each resistor in series.
• Resistors in parallel: The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances: 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...
• Voltage is the same across each resistor in parallel.