College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Surface charge density, denoted as $\sigma$, is the amount of electric charge per unit area on a surface. It is measured in coulombs per square meter ($C/m^2$).
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Surface charge density is given by $\sigma = \frac{Q}{A}$, where $Q$ is the total charge and $A$ is the area.
It can be positive or negative depending on the nature of the charges on the surface.
The electric field just outside a charged conductor is directly proportional to the surface charge density and can be calculated using $E = \frac{\sigma}{\epsilon_0}$.
$\epsilon_0$ (the permittivity of free space) has a value of approximately $8.85 \times 10^{-12} C^2/(N \cdot m^2)$.
Surface charge density plays a crucial role in calculating electric fields for various charge distributions.
Review Questions
How do you calculate surface charge density?
What is the relationship between surface charge density and electric field just outside a conductor?
Why is it important to know if surface charge density is positive or negative?
Related terms
Electric Field: A vector quantity that represents the force per unit charge exerted on a test charge at any point in space.
Permittivity of Free Space ($\epsilon_0$): A physical constant that describes how an electric field affects and is affected by a vacuum. Its value is approximately $8.85 \times 10^{-12} C^2/(N \cdot m^2)$.