A long solenoid of diameter $$0.1$$ m has $$2$$×$$104$$ turns per meter. At the centre of the solenoid, a coil of $$100$$ turns and radius $$0.01$$ m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $$0$$ A from $$4$$ A in $$0.05$$ s. If the resistance of the coil is $$10$$$$π$$$$2$$Ω, the total charge flowing through the coil during this time is

Question

A long solenoid of diameter $$0.1$$ m has  $$2$$×$$104$$  turns per meter. At the centre of the solenoid, a coil of $$100$$ turns and radius $$0.01$$ m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to $$0$$ A from $$4$$ A in $$0.05$$ s. If the resistance of the coil is $$10$$$$π$$$$2$$Ω, the total charge flowing through the coil during this time is

Infinity Learn · Accepted Answer

Given $$n=2$$×$$104$$;$$I=4$$ AInitially I $$=$$ $$0$$ A∴$$Bi=0$$ or ϕ$$i=0Finally$$, the magnetic field at the centre of the solenoid is given $$asBf=$$μ$$onIBf=4$$π×$$10-7$$×$$2$$×$$104$$×$$4Bf=32$$π×$$10-3$$ TFinal magnetic flux through the coil is given as ϕ$$f=nBA$$     $$=100$$×$$32$$π×$$10-3$$×π×$$(0.01)2$$ ϕ$$f=32$$$$π$$$$2$$×$$10-5Tm2Induced$$ charge,$$q=$$|Δϕ|$$R=$$ϕ$$f-$$ϕ$$iR=32$$$$π$$$$2$$×$$10-510$$$$π$$$$2=32$$×$$10-6C=32$$μC

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