chapter 2

2.1 Introduction to Electrostatic Potential

• Potential Energy: Introduced in previous chapters; energy stored when external work is done against forces (spring/gravitational).

• Conservative Forces: Forces like spring, gravitational, and Coulomb are conservative; potential energy is defined with respect to these forces.

• Electrostatic Potential Energy: Defined for charges in an electric field (E). For example, moving charge 'q' in field due to charge 'Q' involves potential energy changes.

2.2 Electrostatic Potential

• Work Done: Moving a test charge 'q' from point R to P against electric force; work done is path-independent due to conservative nature of electrostatic forces.

• Potential Difference: Defined as work done per unit charge arising from movement against electric field, with respect to a reference point (can be zero at infinity).

• Potential Energy Calculation: Electrostatic potential at point is work done in bringing unit positive charge from infinity.

2.3 Potential due to Point Charge

• Potential of a Point Charge (Q): Given by formula

  

  is applicable for both positive and negative charges. Work done moving from infinity to point P accounted.

2.4 Electric Dipole Potential

• Definition: Electric dipole consists of charges +q and -q separated by distance. Both charge and angle between position vector and dipole moment influence potential at point P.

• Potential due to Dipole: Expressed as V(r) = (1 / (4πε₀)) * (p·r̂) / r², where p = dipole moment.

2.5 System of Charges Potential

• Superposition: For systems of multiple charges (q₁, q₂...), potential V at a point determined by contributions from each charge.

2.6 Equipotential Surfaces

• Definition: Surface where potential is constant. Electric field is perpendicular to equipotential surfaces.

2.7 Potential Energy of Charge Systems

• Potential Energy (U): Work done to assemble charges in configuration. For two charges, U = (1 / (4πε₀)) * [(q₁) (q₂) / r].

2.8 Potential Energy in External Fields

• Definition: Potential energy for charge in an external field is U = q*V(r), where V(r) is potential due to external environment.

2.9 Electrostatics of Conductors

• Conductors: Internal electric field is zero; charges reside on surfaces. Potential is uniform throughout conductor's volume.

• Electric Field Relation: Surface field |E| = σ/ε₀, where σ is surface charge density.

2.10 Dielectrics and Polarization

• Dielectrics: Non-conductors polarize in electric fields enhancing potential energy stored in configuration.

• Effect of Polarization: Relationship between induced dipole moments in dielectric and external fields defines dielectric constant K.

2.11 Capacitors and Capacitance

• Capacitance (C): Defined by relation Q = CV; it is the ability to store charge per unit potential difference.

• Capacitance of Parallel Plates: C₀ = ε₀ (A/d), where A is area and d is the separation.

2.12 Capacitor with Dielectric

• Formula Adjustment: Inserting dielectric modifies capacitance: C = K C₀. The dielectric constant K quantifies this change.

2.13 Capacitors in Series and Parallel

• Series: 1/C = 1/C₁ + 1/C₂ + ...; effective capacitance decreases.

• Parallel: C = C₁ + C₂ + ...; effective capacitance increases.

2.14 Work Stored in Capacitors

• Energy Storage (U): U = (1/2) CV², relating stored energy in terms of potential and charge. Energy density in electric field is u = (1/2) ε₀ E².