Linear charge density Calculator
Linear charge density is the amount of electric charge per unit length along a line or curve.
Formula first
Overview
This quantity is used to describe the distribution of electric charge when it is spread along a one-dimensional path, such as a thin wire or a filament. It is defined as the ratio of an infinitesimal charge element to the corresponding infinitesimal length element. In cases where the charge is distributed uniformly, it simplifies to the total charge divided by the total length.
Symbols
Variables
= Linear charge density, dQ = Charge, dl = Length
Apply it well
When To Use
When to use: Use this when calculating the electric field or potential produced by a charged wire, rod, or thin filament where the charge is distributed along a line.
Why it matters: It is essential for solving problems in electrostatics involving non-point charge distributions, which are common in engineering applications like transmission lines and antennas.
Avoid these traps
Common Mistakes
- Confusing linear charge density with surface or volume charge density.
- Assuming the charge density is constant when it actually varies along the length of the object.
One free problem
Practice Problem
A thin wire of length 0.5 meters carries a uniform total charge of 2.0 Coulombs. What is the linear charge density of the wire?
Solve for: lambda
Hint: Divide the total charge by the total length.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.
- Young, H. D., & Freedman, R. A. (2020). University Physics with Modern Physics (15th ed.). Pearson.
- Halliday, D., Resnick, R., & Walker, J. (Fundamentals of Physics)
- NIST CODATA
- IUPAC Gold Book
- Wikipedia: Linear charge density
- Griffiths, David J. (2017). Introduction to Electrodynamics. 4th ed. Cambridge University Press.