Question

If electric potential is constant in a region, electric field in that region is:

• A. finite and constant
• B. zero
• C. infinite
• D. varying

Hint:

No change in potential means no electric field.

Answer 1

The Correct Option is B

Step 1: The link between field and potential.
The electric field is the negative rate of change of potential with distance: \[ E = -\frac{dV}{dx}. \]
Step 2: What constant potential means.
If the potential $V$ has the same value everywhere in the region, then it does not change with position, so its derivative is zero: $\frac{dV}{dx} = 0$.
Step 3: Find the field.
Putting this into the relation, \[ E = -\frac{dV}{dx} = -0 = 0. \]
Step 4: A simple picture to confirm.
Field lines always point from higher to lower potential. With no potential difference anywhere, there is nothing to push a charge, so no field exists.
Step 5: Conclusion.
A region of constant potential has zero electric field. \[ \boxed{\text{zero}} \]