Capacitance (C): Defined as C = Q/V where Q is the charge and V is the voltage.
Parallel Plate Capacitor: Consists of two plates, one with a positive charge and one with a negative charge.
Electric Field in Capacitors
Inside Plates: Electric field (E) is zero on both left and right-side outside plates.
Between Plates: Electric field is defined as σ/ε₀ where σ is charge density and ε₀ is permittivity of free space.
Important Equations
Charge Density (σ): σ = Q/A, where A is the area of the plates.
Electric Field (E): E = σ/ε₀.
Potential Difference (V): V = Ed, where d is the distance between the plates.
Capacitance (C): C = Q/V, which simplifies to C = ε₀A/d.
Relationships
Direct Proportionality: Capacitance (C) is directly proportional to the area (A) of the plates.
Inverse Proportionality: Capacitance (C) is inversely proportional to the distance (d) between the plates.
Key Points
Permittivity (ε₀): Represents how much resistance the electric field encounters in the medium; higher permittivity means greater capacitance.
Area (A): Larger plate area results in higher capacitance because it can store more charge.
Distance (d): Smaller distance between plates results in higher capacitance due to stronger electric field interaction.
Conceptual Understanding
By reducing the distance (d) between plates, the electric field (E) increases, thus increasing capacitance (C).
Increasing the area (A) allows more charge (Q) to be stored, thus increasing capacitance.
Capacitance is a measure of the ability to store charge; it depends on both the physical dimensions and properties of the plates and the medium in which they are placed.
Conclusion
This lecture covers the essential principles of capacitance in parallel plate capacitors, focusing on fundamental equations and relationships that determine their behavior.
Understanding these concepts is crucial for solving problems related to electric fields, potential difference, and charge storage in capacitors.