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Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate 17.8 A/s, the emf in coil 1 is 27.1 mV. (a) What is their mutual inductance? (b) When coil 2 has no current and coil 1 has a current of 4.00 A, what is the flux linkage in coil 2?

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Answer:

Part a)

[tex]M = 1.52 mH[/tex]

Part b)

[tex]\phi = 6.09 \times 10^{-3} Tm^2[/tex]

Explanation:

Part a)

As we know by Faraday's law

[tex]EMF = M \frac{di}{dt}[/tex]

so we will have

[tex]EMF = 27.1 mV[/tex]

[tex]EMF = 27.1 \times 10^{-3} V[/tex]

[tex]\frac{di}{dt} = 17.8 A/s[/tex]

so we will have

[tex]M = \frac{V}{\frac{di}{dt}}[/tex]

[tex]M = \frac{27.1 \times 10^{-3}}{17.8}[/tex]

[tex]M = 1.52 mH[/tex]

Part b)

As we know by Lenz law

[tex]\phi = Mi[/tex]

so we have

[tex]\phi = (1.52 \times 10^{-3})(4)[/tex]

[tex]\phi = 6.09 \times 10^{-3} Tm^2[/tex]

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