A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
Newton's third law applies to the Coulomb force — the...

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the  symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field,...