A thin plastic rod is bent into a circular ring of radius $R$. It i...

Question

A thin plastic rod is bent into a circular ring of radius $R$. It is uniformly charged with linear charge density $\lambda$. What is the magnitude of the electric field at its centre?

Accepted Answer

Step 1: By symmetry, consider the ring as made of many small charge elements $dq$.

Step 2: Each element produces a field at the centre, but for every element there is a diametrically opposite element producing an equal and opposite field.

Step 3: All these field contributions cancel in pairs.

Step 4: Hence, net electric field at the centre of a uniformly charged ring $= 0$.

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