Step 1: Understanding Electric Potential and Electric Field
The electric potential created by a positive charge is inherently positive. This definition stems from the work required to move a unit positive charge from an infinite distance to a specific point.
Conversely, the electric field is derived as the negative gradient of the potential, indicating its direction points towards regions of lower potential.
Step 2: Condition for Zero Electric Field
A net electric field of zero can arise at a point due to the vector summation of individual electric fields. When multiple positive charges are arranged symmetrically, their electric fields can counteract each other at a particular location, resulting in a null net field.
Step 3: Condition for Zero Potential
Electric potential is a scalar quantity and is calculated as the algebraic sum of the potentials from individual charges. Since the potential from each positive charge is always positive, their collective sum cannot equate to zero at any point in space. Therefore, while the electric field can achieve zero, the potential cannot.
Step 4: Conclusion
Option (a) is the correct choice. This is because the net potential at a point cannot be zero, whereas the net electric field can become zero if the vector sum of individual fields cancels out.