In a region of constant potential

Options

A. the electric field is uniform.
B. the electric field is zero.
C. there can be no charge inside the region.
D. the electric field shall necessarily change if a charge is placed outside the region.

Answer

B, C

Explanation

The relation between the electric field (E ) and electric potential (V) is given by:
`E= -(dV)/(dr)` As the electric potential is constant:
`rArr E= -(d("constant"))/(dr)=0`.
Therefore, electric field is zero. When the electric field is zero in a region of space, then electric flux linked with any closed surface within this region will be zero. From Gauss.s law, we can deduce that enclosed charge must also be zero.
Visualise a case of some metallic object. We know that potential everywhere on metallic object remains the same in electrostatics. Hence, its volume can be considered as a region of constant potential and zero electric field. If we place some charge near this metal object then also electric field inside metal remains zero. Hence elecrtric field in the region of constant potential may not change if a charge is placed outside the region. Hence, option (d) is not correct.