Question

(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.
(b) A rectangular coil of area A, having number of turns N is rotated at ' f ' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 rf NBA.

Answer 1

Answer:

Part a)

Mutual inductance of two coaxial coils is given as

$M = \frac{\mu_o \pi r_1^2}{2 r_2}$

Part b)

Rate of change in flux is induced EMF so maximum value of induced EMF is given as

$E = NBA(2\pi f)$

Explanation:

When EMF induced in a coil due the the change in flux of its adjacent coil then this phenomenon is induction of EMF is known as Mutual Inductance

So here we have two coils placed co-axially

Now current due to outer coil magnetic field is given as

$B = \frac{\mu_o i}{2r_2}$

now magnetic flux linked with inner coil is given as

$\phi = B.A$

$\phi = \frac{\mu_o i}{2 r_2} (\pi r_1^2)$

now as per mutual inductance of two coils we have

$M = \frac{\phi}{i}$

$M = \frac{\mu_o \pi r_1^2}{2 r_2}$

Part b)

Magnetic flux linked with the coil placed in uniform magnetic field is given as

$\phi = N B.A$

$\phi = NBA cos\omega t$

now induced EMF is given as rate of change in magnetic flux

so we will have

$\frac{d\phi}{dt} = NBA\omega sin\omega t$

here we know that

$\omega = 2\pi f$

so maximum value of induced EMF is given as

$E_{max} = 2\pi f NBA$

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Topic : induced EMF and mutual inductance

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