Advertisements
Advertisements
Question
Two circular loops, one of small radius r and the other of larger radius R, such that R >> r, are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement.
Advertisements
Solution
Let a current IP flow through the circular loop of radius R. The magnetic induction at the centre of the loop is
BP = `(mu_0I_P)/(2R)`
As, r << R, the magnetic induction BP may be considered to be constant over the entire cross-sectional area of the inner loop of radius r. Hence magnetic flux linked with the smaller loop will be
`Φ_S = B_PA_S = (mu_0I_P)/(2R)pir^2`
Also, ΦS = MIP
∴ M = `Phi_S/I_P = (mu_0pir^2)/(2R)`
APPEARS IN
RELATED QUESTIONS
Define mutual inductance.
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.
The mutual inductance of a pair of adjacent coils is 1.5 H. If the current is one coil changes from 5 A to 10 A in 0.1 s, the rate of change of magnet flux linkage is ______.
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.
Two coils having self inductances L1 = 75 mH and L2 = 55 mH are coupled with each other. The coefficient of coupling (K) is 0. 75. Calculate the mutual inductance (M) of the two coils
The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is ______.
What maximum value of \[M\] follows from \[M=K\sqrt{L_1L_2}\] and \[0\leq K\leq 1\] ?
What is \[M_{21}\] for two coaxial solenoids with the smaller solenoid inside the larger?
What is the magnetic flux through the inner small coil when current \[I_2\] flows in the outer large coil?
