Electrostatics & Capacitance

Understanding Electrostatics

Electrostatics is the study of electric charges at rest. It involves understanding how charges interact with each other and the forces they exert.

• Electric Charge: A property of matter that causes it to experience a force when placed in an electric field. It can be positive or negative.
• Like Charges Repel: Two positive or two negative charges push away from each other.
• Opposite Charges Attract: A positive and a negative charge pull towards each other.

 

Capacitance

Capacitance is the ability of a system to store electric charge. It is measured in farads (F).

• Capacitor: A device that stores electrical energy in an electric field, typically consisting of two conductive plates separated by an insulator.
• Formula: The capacitance $C$ of a parallel-plate capacitor is given by:

$$C = \frac{\varepsilon A}{d}$$

• $\varepsilon$ is the permittivity of the material between the plates.
• $A$ is the area of one of the plates.
• $d$ is the separation between the plates.

 

Factors Affecting Capacitance

• Plate Area: Larger plate area increases capacitance.
• Plate Separation: Smaller separation increases capacitance.
• Dielectric Material: A material with higher permittivity increases capacitance.

 

Energy Stored in a Capacitor

The energy $E$ stored in a charged capacitor is given by:

$$E = \frac{1}{2} C V^2$$

• $C$ is the capacitance.
• $V$ is the voltage across the capacitor.

 

Uses of Capacitors

• Energy Storage: Capacitors can store energy for later use.
• Filtering: Used in electronic circuits to filter out noise.
• Tuning Circuits: Used in radios to select different frequencies.