Electric Field at the Center of a Regular Polygon – Rankers Physics
Topic: Electrostatics
Subtopic: Electric Field

Electric Field at the Center of a Regular Polygon

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 all the corners except one. The magnitude of electric field at the centre of the polygon is
\(\frac{kq(n-1)}{r^2}\)
\(\frac{2kq}{r^2}\)
\(\frac{kqn}{r^2}\)
\(\frac{kq}{r^2}\)

Solution:

A completely symmetric distribution of \(n\) charges has a net field of zero at the center. Removing one charge is equivalent to superimposing a charge of \(-q\) at the empty corner on an otherwise full polygon, which produces a field of magnitude \(\frac{kq}{r^2}\).

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