Electrostatic Potential

Definition

• Electrostatic potential at a point is defined as the amount of work done in bringing a positive test charge of 1 coulomb from infinity to that point without acceleration in the presence of other stationary charges (NCERT Class 12, Chapter - Electrostatics).

Relationship with Electric Field

• Electric field (E) at a point is the negative gradient of the electrostatic potential (V) at that point, i.e., E = -∇V (NCERT Class 12, Chapter - Electrostatics)

Calculation

• For a point charge q, V = kq/r, where k is coulomb’s constant and r is the distance from the charge (NCERT Class 12, Chapter - Electrostatics).
• For a system of charges, the potential at a point is given by the superposition principle, i.e., V = kΣ(qi/ri)

Equipotential Surfaces

• Equipotential surfaces are surfaces in which the potential is constant; hence no net work is done in moving a charge on these surfaces.
• Equipotential surfaces are always perpendicular to the electric field lines.

Potential Energy

Definition

• Electric potential energy (U) of a system of charges is the potential energy stored in the charge distribution due to their relative positions and charges (NCERT Class 12, Chapter - Electrostatics)

Relationship with Electrostatic Potential

• U of a system of charges is equal to the work done in assembling the system from infinity with the final charges at their respective positions.

Calculation

• For a point charges q1 and q2 separated by a distance r, U = k(q1q2)/r, where k is coulomb’s constant (NCERT Class 12, Chapter - Electrostatic potential energy)
• For a system of several point charges, the potential energy is obtained by summing up the potential energy of each pair of charges.

Minima and Maxima

• Minima of electric potential energy correspond to stable equilibrium configurations, while maxima correspond to unstable equilibrium.

Applications of Electrostatic Potential

• Capacitors

  • Capacitance of a capacitor is directly proportional to the potential difference between its plates and inversely proportional to the distance between them (NCERT Class 12, Chapter - Capacitance)

• Dielectrics

  • Presence of a dielectric between capacitor plates reduces the potential difference between them while increasing the capacitance (NCERT Class 12, Chapter - Capacitors and dielectrics)

• Semiconductors

  • Semiconductor devices, like diodes and transistors, operate based on the control of potential barriers and potential energy profiles (NCERT Class 12, Chapter - Semiconductor electronics: materials, devices, and simple circuits)

• Plasmas

  • In plasma physics, electrostatic potential plays a crucial role in understanding various plasma phenomena, like Debye shielding and plasma oscillations.

Electrostatic Potential and Potential Energy Problems

Practice a variety of problems involving:

• Calculation of electrostatic potential and potential energy for different charge configurations.
• Study of the motion of charged particles in electric fields.
• Understanding the stability of charged particle configurations.
• Capacitor and dielectric related problems.
• Analysis of semiconductor devices.