A circular loop of radius R carries charge with uniform linear charge density lambda. The electric field strength at the centre of the loop is proportional to which of the following?

lambda*R
lambda/R
lambda/R²
none of the above

Correct answer: none of the above

Solution

For a uniformly charged circular loop, every charge element has a diametrically opposite element producing an equal and opposite field at the centre. All contributions cancel, so the net electric field at the centre is exactly zero. It is therefore not proportional to lambda*R, lambda/R, or lambda/R²; the correct choice is 'none of the above'.

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