Advertisements
Advertisements
Questions
Derive the expression for the self-inductance of a long solenoid of cross sectional area A and length l, having n turns per unit length.
Obtain an expression for self-inductance of a long solenoid of length l, area of cross-section A having N turns.
Advertisements
Solution
The self-inductance of a solenoid is defined as the magnetic flux to current ratio via the solenoid. It is given by,
L = `phi/I`
Total number of turns in the solenoid,
N = nl
The magnetic field inside the long solenoid,
B = μ0ni
Flux through one turn,
`phi_1 = BA = mu_0niA`
Thus, total flux through N turns,
`phi_t = Nphi_1 = nl xx mu_0niA = mu_0n^2lAi`
Using `phi_t = Li`
where L is the self-inductance of the coil.
∴ `mu_0n^2lAi = Li`
L = `mu_0n^2Al`
APPEARS IN
RELATED QUESTIONS
In a given coil of self-inductance of 5 mH, current changes from 4 A to 1 A in 30 ms. Calculate the emf induced in the coil.
Write the SI unit and dimention of of co-efficient of self induction
Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current goes through them
(d) time constant if one solenoid is connected to one battery and the other is connected to another battery.
Define self-inductance.
The magnetic potential energy stored in a certain inductor is 15 mJ, when the current in the inductor is 40 mA. This inductor is of inductance ____________.
When current i passes through an inductor of self-inductance L, energy stored in it is 1/2. L i2. This is stored in the ______.
An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10-3s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be ______.
An air-cored solenoid, 40 cm long and of cross-sectional area 5 cm2, is tightly wound with 400 turns of copper wire and carries a steady current of 10 A. (a) Calculate the self-inductance of the solenoid. (b) Find the emf induced if the current in the solenoid decreases to zero in 0.2 s.
State the factors on which the magnetic coupling coefficient of two coils depends.
