Gauss's Law Electric Field Calculator | Real-Time Physics Tool

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Gauss's Law Calculator

Select Geometry

Charge (Q)

Enter charge in Coulombs (e.g., 1e-6 for 1μC)

Distance from Center (r)

Distance from center/axis/plane in meters

Permittivity (ε)

C²/N·m²

Permittivity of free space: 8.85×10⁻¹² C²/N·m²

Length/Radius (a)

Radius for sphere/cylinder or half-width for plane

Charge Density Type

Uniform Non-Uniform

Gauss's Law Formula: ∮E·dA = Q_enc/ε₀

For spherical symmetry: E = Q/(4πε₀r²)

Calculation Results

Electric Field (E):

0.00 N/C

Electric Flux (Φ):

0.00 N·m²/C

Enclosed Charge (Q_enc):

0.00 C

Field Direction:

Radially Outward

Formula Applied:

E = Q/(4πε₀r²)

Electric Field Visualization

Visualization Type

Visualization Scale

Calculation History

No calculations yet. Perform a calculation to see history.

Quick Reference

Gauss's Law Applications:

Spherical Symmetry E = Q/(4πε₀r²)
Cylindrical Symmetry E = λ/(2πε₀r)
Infinite Plane E = σ/(2ε₀)
Line Charge E = λ/(2πε₀r)

Common Constants:

ε₀ (Vacuum) 8.85×10⁻¹²

k (Coulomb) 8.99×10⁹

Unit Converter

Charge Conversion

Understanding Gauss's Law and Electric Field Calculations

Gauss's Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. This powerful tool simplifies electric field calculations for symmetric charge distributions.

How to Use This Gauss's Law Calculator

Select the geometry that matches your charge distribution: spherical, cylindrical, planar, or linear symmetry.
Enter the charge value in Coulombs. You can use scientific notation (e.g., 1e-6 for 1 microcoulomb).
Input the distance from the center, axis, or plane where you want to calculate the electric field.
Adjust permittivity if needed (default is the permittivity of free space, ε₀ = 8.85×10⁻¹² C²/N·m²).
Click "Calculate Electric Field" to see instant results including electric field strength, electric flux, and enclosed charge.
Visualize the field using the interactive visualization panel to understand field direction and strength patterns.

Practical Applications of Gauss's Law

Spherical conductors: Calculate electric field inside and outside charged spheres
Cylindrical capacitors: Determine field between coaxial cylinders
Parallel plate capacitors: Find uniform field between charged plates
Transmission lines: Analyze fields around power lines
Semiconductor devices: Model electric fields in MOSFETs and other components

Pro Tip:

Gauss's Law is most effective for problems with high symmetry. The key is choosing an appropriate Gaussian surface where the electric field is either constant or perpendicular to the surface.

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This Gauss's Law calculator helps students, engineers, and physicists solve electromagnetism problems. Related search terms include: electric field calculator, flux calculator, Coulomb's law calculator, electromagnetism simulation, physics problem solver, and electrostatic field tool.