Question

If the electric field in some region of space is zero,
A. it implies that there is no electric charge in that region.
B. it implies that there is electric charge in that region.
C. it does not imply anything concrete about the charges in the region.
D. It means there is discharge in the region.

Answer 1

The above problem can be resolved using the mathematical formula of the electric field in any region. This formula is known as the gauss formula that relates the charge density and the absolute permittivity of free space, where the analysis is being carried out. Moreover, variation in charge density brings to the conclusion about the presence or the absence of electric charges within the space.

Complete step by step answer:
The mathematical formula for the electric field according to the gauss law is given as,
$E = \dfrac{\rho }{{{\varepsilon _0}}}$
Here, $\rho$ and ${\varepsilon _0}$ are the charge density and the permittivity of free space respectively
If the electric field in some region becomes zero, it does make sense that there is no presence of the electric charge.
Rather it implies that there must be the same number of opposite charges present in the particular region. Because according to the given formula, the charge density will become zero along with the electric field.
Therefore, it does not imply anything concrete about the charges in the region

So, the correct answer is “Option C”.

Note:
Try to understand the meaning of an electric field; an electric field is an imaginary line that is formed within any region where there is some sort of electrostatic force is involved. In addition to this, one should be aware of the gauss formula to calculate the electric field in a region, known as the gaussian surface. The charge density also plays a major role to predict the presence of an electric field across the region.