To solve this problem, we need to analyze both the electric field \( E \) and the electric potential \( V \) at the center \( O \) of the given arrangement of charges.
The image shows a symmetric arrangement of charges on a pentagon, with each vertex having a charge \( q \).
Electric Field \( E \):
The electric field due to a point charge at any other point is given by the formula:
E = \frac{kq}{r^2}, where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge.
Due to symmetry, the resultant electric field at the geometric center \( O \) will be zero because the individual electric field vectors from all the charges will cancel out each other.
Therefore, \( E = 0 \).
Electric Potential \( V \):
The electric potential due to a point charge is given by:
V = \frac{kq}{r}.
Electric potentials are scalar quantities and can be added algebraically.
The potential at \( O \) due to each charge is equal and additive because they do not cancel each other as vectors do.
Thus, the net potential \( V \) at the center will be non-zero.
Conclusion:
For the given charges, the electric field \( E \) at the center is zero while the electric potential \( V \) is non-zero.
The correct option is: E = 0; V = \text{Non-zero}.
