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Question

Physics Question on Electromagnetic induction

AA 2 m2 \,m long solenoid with diameter 2 cm2\, cm and 20002000 turns has a secondary coil of 10001000 turns wound closely near its midpoint. The mutual inductance between the two coils is

A

2.4×10−4 H2.4 \times 10^{-4}\,H

B

3.9×10−4 H3.9 \times 10^{-4}\,H

C

1.28×10−3 H1.28 \times 10^{-3}\,H

D

3.14×10−3 H3.14 \times 10^{-3}\,H

Answer

3.9×10−4 H3.9 \times 10^{-4}\,H

Explanation

Solution

Here, l=2ml= 2 m, diameter =2 cm= 2\, cm ∴\therefore radius, r=22=1 cm=1×10−2 m r=\frac{2}{2}=1\,cm =1\times10^{-2}\,m N1=2000,N2=1000N_{1}=2000, N_{2}=1000 Area =πr2=π×(1×10−2)2=\pi r^{2}=\pi\times\left(1\times10^{-2}\right)^{2} =3.14×10−4 m2=3.14\times10^{-4}\,m^{2} Mutual inductance, M=μ0N1N2AlM =\frac{\mu_{0} N_{1}N_{2}A}{l} =4π×10−7×2000×1000×3.14×10−42=\frac{4\pi\times10^{-7}\times2000\times1000\times3.14\times10^{-4}}{2} =3.9×10−4 H=3.9\times10^{-4}\,H