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13 Ιαν 2021 · Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge; Describe line charges, surface charges, and volume charges; Calculate the field of a continuous source charge distribution of either sign
Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge; Describe line charges, surface charges, and volume charges; Calculate the field of a continuous source charge distribution of either sign
As examples, an isolated point charge has spherical symmetry, and an infinite line of charge has cylindrical symmetry. Choose a Gaussian surface with the same symmetry as the charge distribution and identify its consequences. With this choice, →E ⋅ ˆn is easily determined over the Gaussian surface.
In order to calculate the electric field created by a continuous charge distribution we must break the charge into a number of small pieces dq, each of which create an electric field dE. For example, if the charge is to be broken into point charges, we can write: G G. = ∫ = d E. 4 πε ∫. 0. dq. r ˆ. 2 r. where r is the distance from dq vector.
While we were studying the electric field of a point charge, we calculated the electric field that it generates, some R distance away, the electric field at point P, for a positive point charge is radially outward direction. And, we calculated the magnitude of this electric field by applying Coulomb’s law, which was experimental law.
Let \(\Delta q\) be the total charge along a short segment of the curve, and let \(\Delta l\) be the length of this segment. 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 ...
A charge Q is uniformly distributed on a straight-line segment of length L, as shown in Figure 22-3. We wish to find the electric field at an arbitrarily posi-tioned field point P. To calculate the electric field at P we first choose coordinate axes. We choose the x axis through the line charge and the y axis through point P as shown.
