Question

Which of the following options is correct? In a region of constant potential [NCERT Exemplar]
(a) the electric field is uniform.
(b) the electric field is zero.
(c) there can be charge inside the regiofi.
(d) the electric field shall necessarily change if a charge is placed outside the region.

Answer 1

Answer:

E=-dV/dr

since V is constant it can be clearly seen by differentiating constant we will get electric field as zero.

Answer 2

Answer:

Option (b) is accurate, i.e, the electric field is zero.

Explanation:

• When the charger maintains a constant voltage independent of the charge current load, then it is known as constant potential charging.
• The expression of the electric field in the potential difference region is given as;

                                             $E=-\frac{dV}{dx}$

where, dV = potential difference

            dx = small amount of displacement

Now, we know that the region has constant potential so, V = constant

• Thus we can say the electric field will not be uniform as potential is constant, thus eliminating option (a).
• With constant potential (V), the electric field is expressed as;

                                              $E=-\frac{dV}{dx}=0$

And so, the electric field becomes zero.

Thus, the electric field is zero, in the region of constant potential.