Advertisements
Advertisements
Questions
Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other,
Obtain the expression for the the mutual inductance of two long co-axial solenoids S1 and S2 wound one over the other, each of length L and radii r1 and r2 and n1 and n2 number of turns per unit length, when a current I is set up in the outer solenoid S2.
Solution
Consider two long solenoids S1 and S2 of same length (l ) such that solenoid S2 surrounds solenoid 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 = Coefficient of mutual induction of the two solenoids
When current is passed through solenoid S1, an emf is induced in solenoid S2.
Magnetic field produced inside solenoid S1 on passing current through it is given by
B1 = μ0n1I1
Magnetic flux linked with each turn of solenoid S2 will be equal to B1 times the area of cross-section of solenoid S1
Magnetic flux linked with each turn of the solenoid S2 = B1A
Therefore, total magnetic flux linked with the solenoid S2 is given by
Φ21 = B1A × n2l = μ0n1I1 × A× n2l
Φ21 = μ0n1n2AI1
∴ M21 = μ0n1n2Al
Similarly, the mutual inductance between the two solenoids, when current is passed through solenoid S2 and induced emf is produced in solenoid S1, is given by
M12 = μ0n1n2Al
∴ M12 = M21 = M (say)
Hence, coefficient of mutual induction between the two long solenoids is given by
M=μ0n1n2Al
APPEARS IN
RELATED QUESTIONS
An observer to the left of a solenoid of N turns each of cross section area 'A' observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA.
Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 >> r1). Total number of turns in the two solenoids are N1 and N2, respectively.
A magnetic field of 100 G (1 G = 10−4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10−3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m−1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Define mutual inductance between two long coaxial solenoids. Find out the expression for the mutual inductance of inner solenoid of length l having the radius r1 and the number of turns n1 per unit length due to the second outer solenoid of same length and r2 number of turns per unit length.
In what respect is a toroid different from a solenoid?
How is the magnetic field inside a given solenoid made strong?
A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of 20 Ω is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.
A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1.0 × 10−2 T near the centre of the solenoid.
A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the centre of the solenoid is found to be zero. (a) Find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre?
The length of a solenoid is 0.4 m and the number turns in it is 500. A current of 3 amp, is flowing in it. In a small coil of radius 0.01 m and number of turns 10, a current of 0.4 amp. is flowing. The torque necessary to keep the axis of this coil perpendicular to the axis of solenoid will be ______.
