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13 Ιαν 2021 · Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure 1.6.1. Figure 1.6.1: The configuration of charge differential elements for a (a) line charge, (b) sheet of charge, and (c) a volume of charge.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
Using the equations for the flux and enclosed charge in Gauss’s law, we can immediately determine the electric field at a point at height z from a uniformly charged plane in the xy-plane: \[\vec{E}_p = \dfrac{\sigma_0}{2\epsilon_0} \hat{n}. \nonumber\]
Our first step is to define a charge density for a charge distribution along a line, across a surface, or within a volume, as shown in Figure 5.22. Figure 5.22 The configuration of charge differential elements for (a) a line charge, (b) a sheet of charge, and (c) a volume of charge.
If you know the electric field, then you can easily calculate the force (magnitude and direction) applied to any electric charge that you place in the field. An electric field is generated by electric charge and tells us the force per unit charge at all locations in space around a charge distribution.
Arrange positive and negative charges in space and view the resulting electric field and electrostatic potential. Plot equipotential lines and discover their relationship to the electric field. Create models of dipoles, capacitors, and more!
The line charge density \(\rho_l\) at any point along the curve is defined as \[\rho_l \triangleq \lim_{\Delta l \to 0} \frac{\Delta q}{\Delta l} = \frac{dq}{dl} \nonumber \] which has units of C/m. We may then define \(\rho_l\) to be a function of position along the curve, parameterized by \(l\); e.g., \(\rho_l(l)\).
