Wavelength And Frequency

Gauss Law: Gauss law states that the electric flux through any closed surface is proportional to the charge enclosed by the surface. Mathematically:

where is the electric field, is the differential area vector, and is the permittivity of free space.

Now, applying Gauss's law to a uniformly charged thin spherical shell, we can find the electric field at various points:

(A) At an external point (at a distance from the center of the shell): Since the charge distribution is spherically symmetric, we can use a spherical Gaussian surface of radius (where ). The total charge is enclosed within this Gaussian surface, and the electric field at a distance is given by:

so the electric field is:

(B) At an internal point (at a distance from the center of the shell): For a point inside the uniformly charged spherical shell, the electric flux through the Gaussian surface is zero because no charge is enclosed within the Gaussian surface. Thus, the electric field inside the shell is:

(C) At a point on the surface of the shell (at ): At the surface, the electric field will have the same magnitude as at any external point on a spherical shell with radius . Thus, the electric field is: