Gauss's Law Calculator
Calculate electric flux and charge using Gauss's fundamental law of electrostatics
Calculate Electric Flux and Charge
Total electric charge enclosed by the Gaussian surface
Fundamental physical constant: permittivity of free space
Gauss's Law Results
Gauss's Law: ϕ = Q/ε₀ or Q = ϕ × ε₀
Calculation: ϕ = 0.000e+0 C / 8.854e-12 F/m
Applications: Electrostatic analysis, capacitor design, field calculations
Physical Interpretation
Example Calculation
Point Charge in Sphere
Charge: 10 nC
Gaussian surface: Spherical
Application: Electrostatic analysis
Calculation
Q = 10 nC = 10 × 10⁻⁹ C
ε₀ = 8.854 × 10⁻¹² F/m
ϕ = Q/ε₀ = (10×10⁻⁹)/(8.854×10⁻¹²)
ϕ = 1129 V·m
Electric Charge Units
Key Concepts
Flux depends only on enclosed charge, not surface shape
Vacuum permittivity ε₀ is a fundamental constant
Electric flux units: V·m or N·m²/C
Positive charge creates outward flux
Understanding Gauss's Law
What is Gauss's Law?
Gauss's law is a fundamental principle in electrostatics that relates the electric flux through any closed surface to the electric charge enclosed by that surface. It states that the total electric flux is proportional only to the enclosed charge, independent of the surface shape or charge distribution.
Electric Flux Concept
- •Measures electric field "flow" through a surface
- •Positive for outward field, negative for inward
- •Independent of surface area and shape
- •Depends only on enclosed charge
Gauss's Law Equation
ϕ = Q / ε₀
Q = ϕ × ε₀
- ϕ: Electric flux through closed surface (V·m)
- Q: Total electric charge enclosed (C)
- ε₀: Vacuum permittivity (8.854×10⁻¹² F/m)
Important: The law applies to any closed surface (Gaussian surface)
Applications and Examples
Practical Applications
- • Capacitor design and analysis
- • Electric field calculations
- • Charge distribution analysis
- • Electrostatic shielding analysis
- • Conductor and insulator studies
- • Electromagnetic field theory
Common Geometries
- • Spherical surfaces (point charges)
- • Cylindrical surfaces (line charges)
- • Planar surfaces (sheet charges)
- • Cubic surfaces (distributed charges)
- • Irregular closed surfaces
- • Conductor surfaces
Key Insights
Surface Independence:
- Flux independent of surface shape
- Only enclosed charge matters
- Surface can be any closed shape
Charge Distribution:
- Position inside surface irrelevant
- Multiple charges add algebraically
- External charges don't contribute