Q: Three charges 2q , -q ,-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

Ans: (b)

Sol: Let ABC is an equilateral triangle having centre O . Where OA = OB = OC = x (say)

Let three charges 2q , -q ,-q are located at the vertices A , B , C respectively .

Electric field at O due to 2q is $E_{OA} = \frac{1}{4 \pi \epsilon_0} \frac{2q}{x^2}$ (along AO produced)

Electric field at O due to B(-q ) is $E_{OB} = \frac{1}{4 \pi \epsilon_0} \frac{q}{x^2}$ (along OB)

and , Electric field at O due to C(-q) is $E_{OB} = \frac{1}{4 \pi \epsilon_0} \frac{q}{x^2}$ (along OC)

Now , find the resultant field these three field we can see that Electric field at O is not zero .

But , Electric Potential at O is ,

$\large V = \frac{1}{4 \pi \epsilon_0}\frac{2q}{x} + \frac{1}{4 \pi \epsilon_0}\frac{-q}{x} + \frac{1}{4 \pi \epsilon_0}\frac{-q}{x}$

V = 0