Question

three charges -q,+q and +q are placed at the corner of an equilateral triangle of side a the net electric potential at centroid of the triangle​

Answer 1

Given that,

Three charges are -q, q and q.

Side equilateral triangle = a

We know that,

For equilateral triangle ABC,

$AB= BC= CA = a$

$AO=BO=CO=r$

We know that,

Altitude of equilateral triangle is

$h=\dfrac{1}{2}\times\sqrt{3}\times a$

We need to calculate the value of r

Using formula of r

$r=\dfrac{2}{3}h$

Put the value of h

$r=\dfrac{2}{3}\times\dfrac{1}{2}\times\sqrt{3}\times a$

$r=\dfrac{a}{\sqrt{3}}$

We need to calculate the net electric potential at centroid of the triangle​

Using formula of electric potential

$V=k\dfrac{-q}{r}+\dfrac{kq}{r}+\dfrac{kq}{r}$

Put the value into the formula  

$V=k(\dfrac{-q}{\dfrac{a}{\sqrt{3}}}+\dfrac{q}{\dfrac{a}{\sqrt{3}}}+\dfrac{q}{\dfrac{a}{\sqrt{3}}})$

$V=\dfrac{kq}{\dfrac{a}{\sqrt{3}}}$

$V=\dfrac{kq\sqrt{3}}{a}$

Hence, The net electric potential at centroid of the triangle​ is $\dfrac{kq\sqrt{3}}{a}$