Electrostatics Of Conductors

In this scenario, we are dealing with a spherical shell arrangement where the space between the shells is half-filled with a dielectric material and the other half is air. The electric field in this case can be calculated using Gauss's law, which gives the electric field due to a charge distribution in the form: where is the permittivity of the medium in which the field is present, and is the total charge enclosed by a Gaussian surface. For the region between the shells, two materials are present: air (with permittivity ) and dielectric (with permittivity ). - The field in the air region (between the dielectric and the outer shell) is given by the formula:
- The field in the dielectric region (between the inner shell and the dielectric) is given by the formula:
However, because the electric field is uniform throughout the space between the shells, we need to combine the effects of both the dielectric and the air using their effective permittivities. The total permittivity will be , which accounts for the different regions. Thus, the electric field is: which matches option (A).