Considering a group of positive charges, which of the following statements is correct?
Net potential of the system cannot be zero at a point but net electric field can be zero at that point.
Net potential of the system at a point can be zero but net electric field can't be zero at that point.
Both the net potential and the net electric field can be zero at a point.
Both the net potential and the net electric field cannot be zero at a point.
Correct answer:A
Standard Method
Given: A group of positive charges is considered.
Find: Which statement about net electric potential and net electric field is correct.
For a system of positive charges, the potential at a point is
Here, and are positive. Therefore, each term in the sum is positive, so
Hence, the net potential cannot be zero at a point for this group of positive charges.
However, the electric field is related to the gradient of potential, and due to symmetry the net electric field can be zero at some point even when the potential is nonzero. For example, at a point equidistant from suitable positive charges, electric field vectors can cancel while potentials add.
Therefore, the correct option is A.
Field-Potential Interpretation
Given: All charges in the group are positive.
Find: Whether net potential or net electric field can be zero.
The electric field is the gradient of potential. So, zero electric field does not imply zero potential.
For example, at a symmetric point between two identical positive charges, the electric fields due to the two charges are equal in magnitude and opposite in direction, so they cancel. But the potentials are scalar quantities and add algebraically, so the net potential remains positive.
Thus, net electric field can be zero, but net potential cannot be zero.
Therefore, the correct option is A.
Assuming that if the net electric field is zero, then the net potential must also be zero. This is wrong because electric field is a vector and can cancel by direction, whereas potential is a scalar and adds directly. Check vector cancellation and scalar addition separately.
Treating potential like a vector quantity. This is incorrect because all positive charges contribute positive potential at a point, so these contributions do not cancel. Add the potential contributions algebraically, not by direction.
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