Question

lf three charges
+Q, - Q2, +Q3 are placed
at the corners of an equilateral triangles of
Side 'a' then what is the net electric potential at the
centroid.
​

Answer 1

Given:

Three charges +Q , -Q2 , +Q3 are placed at the corner of an equilateral triangle of side a.

To find:

Net Electrostatic Potential at the centroid.

Calculation:

We note that any medium is divided at the centroid in a ratio of 2 : 1.

Height of equilateral triangle be h

$\therefore \: h = \dfrac{ \sqrt{3} }{2} a$

Height is divided by the centroid in the ratio of 2 : 1

So distance of centroid from individual charges located at the vertex will be :

$d = \dfrac{2}{3} \times \bigg \{ \dfrac{ \sqrt{3} }{2} a \bigg \}$

$= > d = \dfrac{a}{ \sqrt{3} }$

So net potential at Centroid :

$P = \dfrac{kQ}{d} + \dfrac{k ( - Q2)}{d} + \dfrac{k(Q3)}{d}$

$= > P = \dfrac{k}{d} \bigg \{Q - Q2 + Q 3 \bigg \}$

$= > P = \dfrac{k}{ (\frac{a}{ \sqrt{3} } )} \bigg \{Q - Q2 + Q 3 \bigg \}$

$= > P = \dfrac{ \sqrt{3} k}{a} \bigg \{Q - Q2 + Q 3 \bigg \}$

Putting value of Coulomb's Constant:

$= > P = \dfrac{ \sqrt{3} }{4\pi\epsilon_{0}a} \bigg \{Q - Q2 + Q 3 \bigg \}$

So, final answer is:

$\boxed{ \bold{P = \dfrac{ \sqrt{3} }{4\pi\epsilon_{0}a} \bigg \{Q - Q2 + Q 3 \bigg \}}}$