MHT CET · Physics · Electrostatics

Three charges \(2 \mathrm{q},-\mathrm{q}\) and -q are located at the vertices of an equilateral triangle. At the centre of the triangle

A the field is zero but potential is non-zero.
B the field is non-zero but potential is zero.
C both field and potential are zero.
D both field and potential are non-zero.

Verified Solution

Answer & Solution

Correct Answer

(B) the field is non-zero but potential is zero.

Step-by-step Solution

Detailed explanation

From charge configuration, at the centre electric field is non-zero. Potential at the centre due to \(2 q\) charge \(V_{2 q}=\frac{2 q}{r}\)

and potential due to -q charge
\(V_{-q}=-\frac{q}{r} \quad(r=\text { distance of centre point })\)
\(\therefore \quad\) total potential \(\mathrm{V}=\mathrm{V}_{2 \mathrm{q}}+\mathrm{V}_{-\mathrm{q}}+\mathrm{V}_{-\mathrm{q}}=0\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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