Question

A regular polygon has n sides each of length l. Each corner of the polygon is at a distance r from
the centre. Identical charges each equal to q are placed at (n - 1) corners of the polygon. What is
the electric field at the centre of the polygon​

Answer 1

Given:

A regular polygon has n sides each of length l. Each corner of the polygon is at a distance r from the centre. Identical charges each equal to q are placed at (n-1) corners of the polygon.

To find:

Electrostatic Field Intensity at the centre of the polygon.

Calculation:

Let's consider a polygon having charges at all it's vertices. In that case , the field intensity at the centre becomes zero. That's because the diametrically opposite charges cancel out the field intensity at the centre.

But here , one of the vertices of the polygon doesn't contain a charge. So , the diametrically opposite charge shall provide net field intensity at the centre.

$\boxed{ \sf{E_{net} = \dfrac{1}{4\pi\epsilon_{0}} \bigg \{ \dfrac{q}{ {r}^{2} } \bigg \}}}$