Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Define mutual inductance.
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?
A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s−1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
The current in a long solenoid of radius R and having n turns per unit length is given by i= i0 sin ωt. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid ant the coil.
In an induction coil, the coefficient of mutual inductance is 6 henry. If a current of 10 ampere in the primary coil is cut-off in `1/1500"s"`, the e.m.f. at the terminals of the secondary coil will be ____________.
If number of turns in primary and secondary coils is increased to two times each, the mutual inductance ______.
There are two coils A and B seperated by some distance. If a current of 2A flows through A, a magnetic flux of 10-2 Wb passes through B (no current through B). If no current passes through A and a current of 1A passes through B, what is the flux through A?
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 ______.
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 ______.
