Two concentric circular coils, $$C1and$$ $$C2are$$ placed in the XY plane. $$C1$$ has $$500$$ turns, and a radius of $$1cm$$ . $$C2$$ has $$200$$ turns and radius of $$20cm$$. $$C2$$ carries a time dependent current $$It=(5t2$$−$$2t+3)A$$ where t is in s . The emf induced in $$C1$$ (in$$ $$mV),at the instant $$t=1s$$ is $$4x$$. The value of x is $$___________$$

Question

Two concentric circular coils, $$C1and$$ $$C2are$$ placed in the  XY plane.  $$C1$$ has  $$500$$ turns, and a radius of $$1cm$$ .  $$C2$$ has $$200$$  turns and radius of  $$20cm$$. $$C2$$  carries a time dependent current $$It=(5t2$$−$$2t+3)A$$ where  t is in s . The emf induced in $$C1$$ (in$$ $$mV),at the instant  $$t=1s$$ is $$4x$$. The value of x is $$___________$$

Infinity Learn · Accepted Answer

Flux through $$1$$ due to $$2$$ $$=$$φ$$=N1B2A1=500200$$μ$$0I2R2$$$$π$$$$R12Induced$$ emf in coil $$1=E=d$$φ$$dt=200$$×$$500$$×$$4$$π×$$10$$−$$7$$×π×$$10$$−$$42$$×$$20$$×$$10$$−$$2$$×dIdt⇒$$4x$$×$$10$$−$$3=200$$×$$500$$×π$$2$$×$$10$$−$$7$$×$$10$$−$$410$$−$$110t$$−$$2$$ Put t $$=$$ $$1$$ s,  ⇒$$x=5.06$$

Magnetic flux and induced emf

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Magnetic flux and induced emf

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Flux through 1 due to 2 =φ=N1B2A1=500200μ0I2R2πR12Induced emf in coil 1=E=dφdt=200×500×4π×10−7×π×10−42×20×10−2×dIdt⇒4x×10−3=200×500×π2×10−7×10−410−110t−2 Put t = 1 s, ⇒x=5.06

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