Question

Considering 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 cannot be zero at a point.
• D. Both the net potential and the net field can be zero at a point.

Hint:

The electric field is related to the gradient of potential, so it is possible for the field to be zero even when the potential is nonzero.

Answer 1

The Correct Option is A

To understand the problem and determine which statement is correct regarding a group of positive charges, let's analyze each option one by one in the context of electrostatics.

1. Net potential of the system cannot be zero at a point but net electric field can be zero at that point:
   • Electric potential is a scalar quantity, which means it is simply algebraically summed. For a group of positive charges, each charge contributes a positive potential at any point, given by the formula \(V = \frac{kq}{r}\) where \(k\) is Coulomb's constant, \(q\) is the charge, and \(r\) is the distance from the charge to the point.
   • Even if the electric field (a vector quantity) from different charges could cancel each other out at a certain point (resulting in zero net electric field), the potential at that point would still be positive since all contributing potentials are from positive charges and add up.
   • This option correctly states that while electric fields can cancel out, the net potential cannot be zero, as potentials from all charges are positive and additive.
2. Net potential of the system at a point can be zero but net electric field can't be zero at that point:
   • This scenario is not possible for a group of only positive charges. As discussed, all positive charges contribute positively to the potential; hence, it cannot be zero.
   • Moreover, electric field can indeed be zero at a point if vectorial contributions from the charges cancel out.
   • This option is incorrect given the scenario.
3. Both the net potential and the net electric field cannot be zero at a point:
   • As previously explained, the electric field can be zero due to vector component cancellation.
   • The statement is correct in indicating that net potential can't be zero, but it is incorrect in saying that an electric field cannot be zero.
   • Hence, this option is partly incorrect.
4. Both the net potential and the net field can be zero at a point:
   • This option is incorrect because while the electric field can be zero, the potential derived from positive charges cannot be zero due to its nature of scalar addition.

Therefore, the correct answer is: Net potential of the system cannot be zero at a point but net electric field can be zero at that point.