Q.

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 ___________

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answer is 5.06.

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Detailed Solution

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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