Question

Three charges \(2q\), \(-q\) 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 not zero
• B. the field is not zero but potential is zero
• C. both field and potential are zero
• D. both field and potential are not zero

Hint:

Potential adds as a scalar and the net charge is zero. Field adds as a vector, and the two negative fields do not cancel the positive one.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Potential is a scalar sum, while electric field is a vector sum.

Step 2: Potential
At the centre, all vertices are at equal distance \(r\), so \(V=\dfrac{k(2q-q-q)}{r}=0\).

Step 3: Field
The field of \(2q\) points away from its vertex with magnitude \(\dfrac{2kq}{r^{2}}\). The two \(-q\) fields have magnitude \(\dfrac{kq}{r^{2}}\) each, directed towards their vertices at \(120^{\circ}\) apart.

Step 4: Resultant
The resultant of the two equal fields at \(120^{\circ}\) is \(\dfrac{kq}{r^{2}}\), and it points in the same direction as the field of \(2q\), so the net field is \(\dfrac{3kq}{r^{2}}\ne0\).

Final Answer:
The field is not zero but the potential is zero. \[ \boxed{\text{(B) }\text{the field is not zero but potential is zero}} \]