A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

Question

A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

Infinity Learn · Accepted Answer

Directions of currents in two parts are different, so directions of magnetic fields due to these currents are opposite. Also, applying Ohm's law across AB,$$i1R1=i2R2$$⇒$$i1l2=i2l2$$∵$$R=$$ρlA Also, $$B1=$$μ$$04$$π×$$i1l1r2$$ and $$B2=$$μ$$04$$π×$$i2l2r2($$∵$$l=r$$θ$$)$$∴$$B2B1=i1l1i2l2=1Hence$$, two field induction's are equal but of opposite direction. So, resultant magnetic induction at the centre is zero and is independent of θ.

A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle $θ$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

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