22.10
While studying the motion of water through a pipe, infinitesimal volume elements of water are considered. These elements, although small compared to the total volume of the water, contain many molecules. This large number makes it possible to consider their collection a continuous element.
Similarly, although the charge is quantized, a part of a system's total charge can be considered a continuous element. It contains many individual charges but is small enough compared to the total number of charges in the system. Such an approximation is called a continuous charge distribution.
For example, for a charged metallic rod, the charge per unit line element determines the electric field. The principle of superposition gives the rod's electric field as a line integral over its length.
When a plane is charged, the amount of charge per unit surface area determines its field, a surface integral over its entire surface.
When a volume of charge is studied, the charge density per unit volume determines the field, a volume integral over the entire volume.
Stel je een emmer water voor. Het bevat veel moleculen, in de orde van 1026 moleculen. Dus hoewel het op microscopisch niveau discrete elementen (mole…
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