Chapter 2 Electrostatic Potential and Capacitance

Electrostatic Potential

Consider electrostatic potential as the gravity field equivalent of altitude on an electric scale. When a charged particle is moved against an electric field, it acquires electrostatic potential, just like when an item is lifted against gravity. Volts (V) are used to measure this potential.

Formula: $V = W/q$

Here, $V$ represents electrostatic potential, $W$ is the work done in moving the charge, and $q$ is the magnitude of the charge.

Potential Due to a Point Charge

Consider a positive point charge $Q$ . The electrostatic potential ( $V$ ) at a distance ( $r$ ) from the charge is given by

V=kQ/r

Here, $k$ is Coulomb’s constant ( $8.99×10^9 Nm^2/C^2$ ).

Potential Due to a System of Charges

When dealing with multiple charges, the total potential at a point is the algebraic sum of potentials due to individual charges.

$V_{total} = V_{1} + V_{2} + \dots + V_{n}$

Equipotential Surfaces

Equipotential surfaces are fascinating landscapes where every point boasts the same potential. The movement of charges on these surfaces requires no work.

Equipotential surfaces aid in visualizing electric field lines, always perpendicular to these surfaces.

Electrostatic Potential Energy

The electrostatic potential energy ( $U$ ) of a system of charges is a measure of the work done in assembling the system from infinity.

U=q⋅V

Here, $q$ is the charge, and $V$ is the potential.

Capacitance

Capacitance ( $C$ ) quantifies a capacitor’s ability to store charge. It’s defined as the ratio of the charge ( $Q$ ) on one plate to the potential difference ( $V$ ) between the plates.

$C = Q/v$

Capacitors and Capacitance

Types of Capacitors:

Parallel Plate Capacitor: Comprising two parallel plates with a dielectric material in between.
Spherical Capacitor: Involving a conducting sphere and a surrounding concentric spherical shell.
Cylindrical Capacitor: Composed of a central cylindrical conductor and an outer cylindrical shell.

Formulas

Parallel Plate Capacitor: $C = ε ^{0} A/d$
Spherical Capacitor: $C = 4 π ε ^{0} ab/b-a$
Cylindrical Capacitor: $C = 2 π ε ^{0} l/ln(b/a)$