Question

Doesn't guass's law only finds the electric field due to the charge enclosed and since we draw the gaussian surface inside the sphere where there is no charge, wouldn't it be wrong to simply say that the electric field due to the whole hollow sphere is zero even though we aren't drawing the gaussian surface around the charge?

Answer 1

Gauss's Law shows that the electric field inside a hollow charged sphere is zero because the charge enclosed by the Gaussian surface drawn inside is zero, leading to zero electric flux and, consequently, a zero electric field in that region.

Step-by-step explanation:

The student is exploring the application of Gauss's Law and its ability to determine the electric field inside a hollow charged sphere. Indeed, Gauss's Law is based on the concept of electric flux through a closed surface, which indirectly helps us determine the electric field.

The crucial aspect here is choosing an appropriate Gaussian surface with symmetry that corresponds to the charge distribution. When a Gaussian surface is drawn inside a hollow charged sphere, the charge enclosed is zero, as there are no charges within the volume of the Gaussian surface.

According to Gauss's Law, the net flux is proportional to the charge enclosed by the Gaussian surface (q_enc). Since the charge inside the Gaussian surface is zero, the electric flux through the surface is also zero. Consequently, the electric field inside a hollow charged sphere is zero, because the electric field is the cause of electric flux.

This conclusion follows from the fact that electric fields originate and terminate on charges, and since there are no charges inside the sphere to originate or terminate electric field lines, the field must be zero.