Electric Charges and Fields Formulas

Understanding the Basics of Electric Charges and Fields

Posted by Lecture Home on November 11, 2024

This guide covers essential terms and notations in electricity and electric fields, including quantization of charge, Coulomb's Law, gravitational force, electric flux, dipole moment, and Gauss's Law. These concepts form the foundation of electrostatics in physics.

Basic Notations and Their Units

  • e = Elementary charge, 1.602192 × 10–19 C
  • me = Mass of electron, 9.11 × 10–31 kg
  • q = Charge (SI unit: Coulomb, C)
  • 1 C = 6 × 1018 electrons
  • 1 μC (micro coulomb) = 10–6 C
  • ε0 = Permittivity of free space, 8.854 × 10–12 C2 N–1 m–2



Quantization of Charge

Main Formula: q = ne

Where:

  • q = Charge
  • n = Number of electrons
  • e = Elementary charge on one electron

Coulomb's Law

Main Formula: F = k |q1 q2| / r2

Where:

  • F = Force between two charges
  • q1 and q2 = Charges
  • r = Distance between charges
  • k = Constant, 1 / (4π ε0)

Gravitational Force

Main Formula: F = -G |m1 m2| / r2

Where:

  • F = Force between two masses
  • m1 and m2 = Masses of objects
  • r = Distance between charges
  • G = Gravitational constant

Electric Field

Main Formula: E = k Q / r2

Where:

  • E = Electric field
  • Q = Charge producing the field
  • r = Distance between charges



Relation Between Force and Electric Field

Main Formula: F(r) = q E(r)


Acceleration of the Electron

Main Formula: ae = eE / me

Where:

  • me = Mass of electron
  • e = Charge of one electron
  • E = Electric field

Electric Flux

Main Formula: Δϕ = E ⋅ ΔS cosθ

Where:

  • Δϕ = Electric flux
  • E = Electric field
  • ΔS = Area element

Field of an Electric Dipole

On Axis: E = k (4 q a) / r3

On Equatorial Plane: E = -k (2 q a) / r3


Dipole Moment

Main Formula: p = q × 2a


Torque on a Dipole

Main Formula: τ = p × E




Surface Charge Density

Main Formula: σ = ΔQ / ΔS


Gauss's Law

Main Formula: Δϕ = E ⋅ ΔS = k q ΔS / r2 = q / ε0


Field Due to a Uniformly Charged Spherical Shell

  • Outside the Shell: E = k q / r2
  • Inside the Shell: E = 0

Download the Complete Formula List

If you need all these formulas in one document, download the complete list from the link below:

Download Formula List

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