Choose the correct statement: Three charges 2q, -q, -q are located at…

The correct answer is Option (2) → potential is zero but the field is non-zero

The centroid G is at the same distance \( r \) from all three vertices. Potential is a scalar, so the three potentials add as numbers; the field is a vector, so the three fields add by direction.

Potential at G

    \( \displaystyle V = \frac{k(2q)}{r} + \frac{k(-q)}{r} + \frac{k(-q)}{r} = \frac{k(2q - q - q)}{r} = 0 \)

Field at G (let \( E = kq/r^{2} \)), with the charge 2q at vertex A and the charges -q at B and C:

    \( \text{From } 2q \text{ at A: } 2E, \text{ directed away from A} \)
    \( \text{From } -q \text{ at B: } E, \text{ towards B} \)
    \( \text{From } -q \text{ at C: } E, \text{ towards C} \)

The directions from G towards B and towards C are \( 120^\circ \) apart, so their two fields add to a single field \( E \) along the bisector, which points away from A.

    \( \displaystyle E_{\mathrm{net}} = 2E + E = 3E = \frac{3kq}{r^{2}} \ne 0 \)

So the potential is zero but the field is not.