electric field due to volume charge distribution with explinations
Answers
The charge distributions we have seen so far have been discrete: made up of individual point particles. This is in contrast with a continuous charge distribution, which has at least one nonzero dimension. If a charge distribution is continuous rather than discrete, we can generalize the definition of the electric field. We simply divide the charge into infinitesimal pieces and treat each piece as a point charge.
Note that because charge is quantized, there is no such thing as a “truly” continuous charge distribution. However, in most practical cases, the total charge creating the field involves such a huge number of discrete charges that we can safely ignore the discrete nature of the charge and consider it to be continuous. This is exactly the kind of approximation we make when we deal with a bucket of water as a continuous fluid, rather than a collection of H
2
O molecules.
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 5.6.1.
Figure a shows a long rod with linear charge density lambda. A small segment of the rod is shaded and labeled d l. Figure b shows a surface with surface charge density sigma. A small area within the surface is shaded and labeled d A. Figure c shows a volume with volume charge density rho. A small volume within it is shaded and labeled d V. Figure d shows a surface with two regions shaded and labeled q 1 and q2. A point P is identified above (not on) the surface. A thin line indicates the distance from each of the shaded regions. The vectors E 1 and E 2 are drawn at point P and point away from the respective shaded region. E net is the vector sum of E 1 and E 2. In this case, it points up, away from the surface.
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