Simple circuit

Consider the above circuit formed using a battery of emf \(E\) and a wire with uniform resistance \(R\). The wire is bent in the shape of a circular loop.

A small charge \(q\) is carried in clockwise direction in this loop with constant angular velocity \(\omega\). Let \(W\) be the average work done by us to carry the charge from point A to B in each cycle.

What is the value of \(W\)?

Details and Assumptions:

  • The electric field of \(q\) has no effect on already existing current.

  • No chemical work is done by the battery on charge \(q\).

  • Resistance of wire is present against this moving charge.


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