Advertisements
Advertisements
Question
Consider two concentric circular coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centers coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.
Advertisements
Solution
Coefficient of mutual induction − consider two coils P and S. Suppose that a current I is flowing through the coil P at any instant i.e.,
Φ ∝ I
Φ = MI… (i)
If ‘e’ is the induced emf produced in the S-coil, then
`e=(dphi)/dt=-d/dt(MI)=-M(dl)/dt`
Mutual Inductance of two concentric coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centers coinciding with each other:
Consider two circular coil S1 and S2 of same length l, such that coil S2 surrounds coil S1 completely
Let
n1 − Number of turns per unit length of S1
n2 − Number of turns per unit length of S2
I1 − Current passed through solenoid S1
Φ21 − Flux linked with S2 due to current flowing through S1
Φ21 ∝ I1
Φ21 = M21I1
Where M21 is the coefficient of mutual induction of the two coils
When current is passed through S1, an emf is induced in S2.
Magnetic field produced inside S1 on passing current through it,
B1 = μ0n1I1
Magnetic flux linked with each turn of S2 will be equal to B1 times the area of the cross-section of S1.
Magnetic flux linked with each turn of the S2 = B1A
Therefore, total magnetic flux linked with the S2,
Φ21 = B1A × n2l = μ0n1I1 × A× n2l
Φ21 = μ0n1n2AlI1
∴ M21 = μ0n1n2Al
Similarly, the mutual inductance between the two coils, when current is passed through coil S2 and induced emf is produced in coil S1, is given by
M12 = μ0n1n2Al
∴M12 = M21 = M (say)
Hence, coefficient of mutual induction between the two coil will be
|
`M=mu_0n_1n_2Al` |
APPEARS IN
RELATED QUESTIONS
In an experiment, two coils c1 and c2 are placed close to each other. Find out the expression for the emf induced in the coil c1 due to a change in the current through the coil c2.
A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Explain the phenomenon of mutual induction.
In mutual induction, the main current remains same because ____________.
Two different wire loops are concentric and lie in the same plane. The current in the outer loop (I) is clockwise and increases with time. The induced current in the inner loop.
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon the ______.
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to ______.
A rectangular coil of wire 50 turn each of area 6 x 10-4 m2 is freely suspended in a field of 3 x 10-2 Wb / m2. Calculate the current flowing through the coil when it deflects through 60°, when torsional constant is 3.82 x 10-6 SI unit.
The value of mutual inductance of two coils is 6 mH. The current in one of the coil changes from 6 A to 1 A in 0.2 second so that e.m.f. is induced in the other coil. If the resistance of the coil is 6 Ω, the value of induced charge passing through the coil is ______.
