Infinite Uniformly Charged Plane and Electric Field

• Infinite uniformly charged plane: Produces a constant electric field.
• Electric field lines: Straight and parallel; should be of the same size.
• Magnitude: Given by E = 2 * Coulomb's constant * π * charge density (σ).*

Charge Density (σ)

• Defined as σ = Q/A where Q is the total charge and A is the area.
• For an infinite plane, A is infinite, making σ difficult to work with directly.

Non-Infinite Planes Approximation

• Non-infinite planes with finite area can approximate an infinite plane near the center.
• Allows examination of voltage and charge properties.

Parallel Plate Capacitor

Setup

• Two plates, both with area A, separated by distance d.
• Charge on plates: +Q on one plate, -Q on the other.

Electric Field Between Plates

• Combination of fields: Superposition of fields from both plates.
  • Both fields are constant near the center.
  • Fields bulge out towards the edges.
• Direction: Field from positive plate goes away; field from negative plate goes towards.
• Total Electric Field (E): E_total = 4KπQ/A
  • K: Coulomb’s constant
  • Q: Charge
  • A: Area

Voltage Difference Across Plates

Definition

• Voltage (V): Electrical potential energy per charge.
• Voltage difference (Vₐ - Vᵦ): Amount of work needed to move a charge from one plate to another against the electric field.
• Equation: ΔV = E * d
  • d: Distance between plates
  • Units: Joules per coulomb (Volts)*

Relationship Between Charge (Q) and Voltage (V)

• Derived formula: Q = (A/4Kπd) * V
• Proportional relationship between voltage and charge.
• Capacitance (C): C = A / (4Kπd)
  • Farad: Unit of capacitance.
  • Formula rewritten: Q/V = C*

Additional Concepts

• Permittivity of Free Space (ε₀): ε₀ = 1/(4Kπ)
• Capacitors: Devices storing electrical energy; characterized by their capacitance and voltage relationship.

Implications and Applications

• Given plate area and separation, amount of charge (Q) and voltage (V) can be determined.
• Practical applications in circuits where voltage determines charge transfer.