Physics Formulas Electrostatics

Physics Formulas for Electrostatics

Introduction to Electrostatics

Electrostatics is the branch of physics that deals with the study of electric charges at rest. It encompasses the principles and laws governing electric fields, forces, and potentials. Electrostatics is fundamental in various applications, including capacitors, electrical insulation, and many real-world technologies.

Basic Electrostatic Principles

Electrostatic phenomena are governed by the following fundamental principles:

Like charges repel, and opposite charges attract.
Electric charge is quantized and conserved.
Electrostatic force acts along the line joining two charges.
The electric field exerts a force on other charges present in the field.
Work is required to move a charge in an electric field, leading to potential energy.

Key Electrostatic Formulas

Coulomb’s Law

Coulomb’s law describes the electrostatic force between two point charges:

\[ F = k \frac{q_1 q_2}{r^2} \]

where:

F = electrostatic force (N)
k = Coulomb’s constant (\( 8.99 \times 10^9 \) N·m²/C²)
q₁, q₂ = magnitudes of the charges (C)
r = distance between the charges (m)

Example: If two charges \( q_1 = 3C \) and \( q_2 = -2C \) are separated by 4m, the force between them is:

\[ F = \frac{(8.99 \times 10^9) (3 \times -2)}{4^2} \]

\[ F = -3.37 \times 10^9 N \]

The negative sign indicates an attractive force.

Electric Field

The electric field due to a point charge is given by:

\[ E = \frac{k q}{r^2} \]

where:

E = electric field (N/C)
q = charge creating the field (C)
r = distance from the charge (m)

Example: A charge of 5C is placed at a point. Find the electric field at 3m away.

\[ E = \frac{(8.99 \times 10^9) (5)}{3^2} \]

\[ E = 4.99 \times 10^9 N/C \]

Electric Potential

Electric potential at a point due to a charge is:

\[ V = \frac{k q}{r} \]

where:

V = electric potential (V)
q = charge (C)
r = distance from charge (m)

Example: The electric potential 2m away from a 6C charge is:

\[ V = \frac{(8.99 \times 10^9) (6)}{2} \]

\[ V = 2.69 \times 10^{10} V \]

Gauss’s Law

Gauss’s law states:

\[ \oint E dA = \frac{Q}{\varepsilon_0} \]

where:

E = electric field (N/C)
dA = infinitesimal area element
Q = charge enclosed (C)
\( \varepsilon_0 \) = permittivity of free space (\(8.85 \times 10^{-12} \) C²/N·m²)

Capacitance

Capacitance of a parallel plate capacitor:

\[ C = \frac{\varepsilon_0 A}{d} \]

where:

C = capacitance (F)
A = plate area (m²)
d = separation distance (m)

Energy Stored in a Capacitor

The energy stored in a capacitor is given by:

\[ U = \frac{1}{2} C V^2 \]

where:

U = stored energy (J)
C = capacitance (F)
V = voltage across capacitor (V)

Applications of Electrostatics

Electrostatics is applied in:

Capacitors: Used in electronic circuits for energy storage.
Photocopiers and Laser Printers: Use electrostatic charges to transfer ink.
Electrostatic Precipitators: Remove pollutants from industrial emissions.
Lightning: A natural electrostatic discharge.
Touchscreens: Many modern touchscreens work on electrostatic principles.
Defibrillators: Use electric charge to restore heart rhythm.

Conclusion

Electrostatics plays a crucial role in physics and technology. Understanding its formulas and principles helps in solving real-world problems and designing electronic devices. From capacitors in circuits to the static charge that makes hair stand up, electrostatics is everywhere around us.