Electric Field at the Center of a Regular Polygon – Rankers Physics

Electric Field: Practice Problem & Solution

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 Explained:

To solve this problem, we apply the core principles of Electric Field. Understanding the underlying formula is key to arriving at the correct answer below:

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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