Question

For a group of positive charges, which of the following statements is correct?

• A. Net potential of the system cannot be zero at a point, but net electric field can be zero at that point.
• B. Net potential of the system at a point can be zero, but net electric field can't be zero at that point.
• C. Both the net potential and the net electric field can be zero at a point.
• D. Both the net potential and the net electric field cannot be zero at a point.

Hint:

- The electric potential is a scalar and cannot be zero for a system of only positive charges.
- The electric field is a vector and can be zero if the fields cancel out symmetrically.

Answer 1

The Correct Option is A

Step 1: Understanding Electric Potential and Electric Field
The electric potential due to a positive charge is always positive because potential is defined as the work done to bring a unit positive charge from infinity to that point.
The electric field, on the other hand, is the negative gradient of potential, meaning that it points in the direction of decreasing potential.
Step 2: Condition for Zero Electric Field
The net electric field at a point can be zero due to the vector nature of electric fields. If multiple positive charges are arranged symmetrically, their electric fields can cancel each other out at a specific point, making the net electric field zero.
Step 3: Condition for Zero Potential
The net potential is a scalar quantity and is the algebraic sum of the potentials due to individual charges. Since the potential due to each positive charge is always positive, their sum cannot be zero at any point in space. This means that while the electric field can be zero, the potential cannot be zero.
Step 4: Conclusion
The correct answer is (a) because the net potential cannot be zero at a point, but the net electric field can be zero if the vector sum of fields cancels out.