Charge physics calculator
Let V 1, V 2, …, V N V 1, V 2, …, V N be the electric potentials at P produced by the charges q 1, q 2, …, q N, q 1, q 2, …, q N, respectively. What is the net electric potential V at a space point P from these charges? Each of these charges is a source charge that produces its own electric potential at point P, independent of whatever other changes may be doing. Consider a system consisting of N charges q 1, q 2, …, q N. Just as the electric field obeys a superposition principle, so does the electric potential. As noted earlier, this is analogous to taking sea level as h = 0 h = 0 when considering gravitational potential energy U g = m g h U g = m g h. It is the potential difference between two points that is of importance, and very often there is a tacit assumption that some reference point, such as Earth or a very distant point, is at zero potential. Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. The total field is the vector sum of the fields from each of the two charge elements (call them and , for now):īecause the two charge elements are identical and are the same distance away from the point where we want to calculate the field, , so those components cancel.Check Your Understanding What is the potential inside the metal sphere in Example 7.10? The symmetry of the situation (our choice of the two identical differential pieces of charge) implies the horizontal ( )-components of the field cancel, so that the net field points in the -direction. The electric field for a line charge is given by the general expression We will check the expression we get to see if it meets this expectation.
Solutionīefore we jump into it, what do we expect the field to “look like” from far away? Since it is a finite line segment, from far away, it should look like a point charge. The electric field at point can be found by applying the superposition principle to symmetrically placed charge elements and integrating. 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 1.5.1.įigure 1.5.2 A uniformly charged segment of wire.
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 H2O molecules. 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. Note that because charge is quantized, there is no such thing as a “truly” continuous charge distribution.
We simply divide the charge into infinitesimal pieces and treat each piece as a point charge. If a charge distribution is continuous rather than discrete, we can generalize the definition of the electric field. This is in contrast with a continuous charge distribution, which has at least one nonzero dimension. The charge distributions we have seen so far have been discrete: made up of individual point particles. Calculate the field of a continuous source charge distribution of either sign.Describe line charges, surface charges, and volume charges.Explain what a continuous source charge distribution is and how it is related to the concept of quantization of charge.By the end of this section, you will be able to: