Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle α at the centre C. The magnitude of magnetic field due to PQRS at centre C is

Question

Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle α at the centre C. The magnitude of magnetic field due to PQRS at centre C is

Infinity Learn · Accepted Answer

The straight portions PQ and RS do not produce magnetic field at C. Only the curved portion QR produces a magnetic field at C. Refer to Fig.Since the current dl is perpendicular to position vector r, the magnetic field at C by $$Biot-Savart$$ law $$isdB=$$μ$$04$$$$π$$Idl $$sin$$⁡$$90r2=$$μ$$04$$$$π$$I×(rd$$θ$$)r2$$ $$($$∵$$dl=rd$$θ$$_)=$$μ$$0I4$$$$π$$rdθ$$B=$$∫$$0$$α$$1dB=$$μ$$0I4$$$$π$$r∫$$0$$αdθ$$=$$μ$$0I$$α$$4$$$$π$$rSo the correct choice is $$(4).

Figure shows a wire PQRS carrying a current I. Portions PQ and RS are straight and QR in a circular arc of radius r subtending an angle $α$ at the centre C. The magnitude of magnetic field due to PQRS at centre C is

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