A coil with $$1500$$ turns, a radius of $$5.0$$ cm and a resistance of $$12$$Ω surrounds a solenoid with $$250$$ $$turns/cm$$ and a radius of $$4$$ cm; see figure. The current in the solenoid changes at a constant rate from $$0$$ to $$20$$ A in $$0.10$$ s. The magnitude of the induced current (in$$ $$A) in the $$1500$$ turn coil is $$($$ Take π$$2=10$$, Neglect self inductance of the $$coil)$$

Question

A coil with $$1500$$ turns, a radius of $$5.0$$ cm and a resistance of $$12$$Ω surrounds a solenoid with $$250$$ $$turns/cm$$ and a radius of $$4$$ cm; see figure. The current in the solenoid changes at a constant rate from $$0$$ to $$20$$ A in $$0.10$$ s. The magnitude of the induced current (in$$ $$A) in the $$1500$$ turn coil is $$($$ Take π$$2=10$$,  Neglect self inductance of the $$coil)$$

Infinity Learn · Accepted Answer

ε$$=1500$$×ddtμ$$0ni$$×π×$$4.01002=1500$$×$$4$$π×$$10$$−$$7$$×$$25010-2$$×$$200.1$$×π×$$4.0$$×$$4.0104i=$$ε$$R=6000$$$$π$$$$2$$×$$5000$$×$$103$$×$$10$$−$$712$$×$$(4.0)2104i=4A$$

Magnetic flux and induced emf

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Magnetic flux and induced emf

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ε=1500×ddtμ0ni×π×4.01002=1500×4π×10−7×25010-2×200.1×π×4.0×4.0104i=εR=6000π2×5000×103×10−712×(4.0)2104i=4A

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