Let's analyze the situation step by step:
1. **Electric Field:**
- The electric field at a point due to a charge is given by \( \mathbf{E} = \frac{kQ}{r^2} \) where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the distance from the charge to the point of interest.
- The electric field due to multiple charges is the vector sum of the fields due to each charge.
- In an equilateral triangle with charges \( 2q \), \( -q \), and \( -q \) at its vertices, the symmetry of the arrangement leads to the electric field at the center not canceling out completely due to the unequal magnitudes of the charges.
2. **Electric Potential:**
- The electric potential at a point due to a charge is given by \( V = \frac{kQ}{r} \).
- The total potential at the center of the triangle is the sum of the potentials due to each charge.
- For an equilateral triangle, the distances from the center to each vertex are equal, so the potential contributions add up directly.
Given these points:
- The electric field at the center is not zero because the charges are not equal, so their fields do not cancel out completely.
- The electric potential at the center, however, is zero because the net contribution from the charges cancels out due to symmetry, considering the charges and distances.
Therefore, the correct answer is:
**B. The field is non-zero but the potential is zero.**
