Linear Charge Density & Gauss's Law Calculator

Electrodynamics, Gauss's Law & Linear Charge Density Metrology

Linear Charge Density represents the quantity of electric charge distributed per unit length along a 1D conductor or wire:

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• Universal Linear Charge Conversion Formulas (SI Standards)**:

1 C/m = 10^6 µC/m = 10^9 nC/m = 10^12 pC/m

λ_C/ft = λ_C/m × 0.3048 | λ_C/in = λ_C/m × 0.0254

1 statC/cm = 3.335641 × 10^-8 C/m 1 µC/m = 29.9792 statC/cm

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• Gauss's Law for an Infinite Line of Charge**:

E · dA = Q_enc_0 E(r) × (2π r L) = (λ L) / (_0)

E(r) = (λ) / (2π _0 r) = (2 k_e λ) / (r)

Q_total = λ × L (Total Enclosed Charge in Coulombs)

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• Standard Electrodynamic & Physical Benchmarks**:

• DNA Double Helix Backbone: 0.59 nC/m 590 pC/m 0.59 e^- per Ångström

• Synchrotron Proton Beam: 5.0 nC/m 5,000 pC/m 3.12 × 10^10 protons/m

• Precipitator Corona Wire: 1.0 µC/m 1,000 nC/m E(0.1m) = 179.8 kV/m

• HV Transmission Line: 10.0 µC/m 10,000 nC/m E(2.0m) = 89.88 kV/m

How to Use This Calculator

Enter your Linear Charge Density (λ) (e.g. 10 in λ), From Linear Charge Density Unit — choose from Microcoulombs per Meter (µC/m = 10⁻⁶ C/m - Power Lines), Coulombs per Meter (C/m - SI Base Unit), Nanocoulombs per Meter (nC/m = 10⁻⁹ C/m - Biophysics), To Linear Charge Density Unit — choose from Nanocoulombs per Meter (nC/m), Coulombs per Meter (C/m), Microcoulombs per Meter (µC/m), Line Conductor Length (L in meters) (e.g. 100 in m), Radial Distance to Field Point (r in meters) (e.g. 2.0 in m), and Electrodynamic & Physical Benchmark — choose from Custom Linear Charge System, High-Voltage Transmission Line (10.0 µC/m) → 10,000 nC/m | Q = 1.0 mC (100m) | E(2m) = 89.88 kV/m, Industrial Precipitator Corona Wire (1.0 µC/m) → 1,000 nC/m | E(0.1m) = 179.8 kV/m (Corona discharge). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Total Enclosed Charge: Q = lambda * L (in Coulombs)

Gauss's Law Radial Electric Field: E(r) = lambda / (2pieps_0r) = (2k_e*lambda) / r

Worked Example

A power transmission engineer evaluating a 10.0 µC/m high-voltage transmission line calculates that at a 2.0 m distance from the conductor, the radial electrostatic field is 89.88 kV/m, safely below the 3,000 kV/m dielectric breakdown threshold of ambient air.

Understanding Your Result

Unit conversions are exact by definition within a given measurement system (e.g., 1 km = exactly 1,000 m). Cross-system conversions (metric to imperial) use defined exchange factors: 1 inch = exactly 2.54 cm; 1 pound = 0.45359237 kg. Round your converted result to match the precision of your original measurement — expressing more decimal places than your input justifies implies false accuracy. For regulatory, legal, or safety-critical applications, verify which measurement system is required by the applicable standard.