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A battery is joined across two points A and B on the rim of a uniform circular conducting ring of radius r and resistance R. Suppose one of the two arcs AB makes an angle θ at the centre. The magnetic field at the centre produced by the current in the ring is

1. proportional to 2(180° − θ)
2. inversely proportional to r
3. zero only when θ = 180°
4. zero for every value of θ

Correct answer: zero for every value of θ

Solution

The two arcs are in parallel; each arc's current is inversely proportional to its length (resistance) while its field contribution is proportional to the angle it subtends. The products are equal and oppositely directed, so the net field at the centre is zero for every value of theta.

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