Define self-inductance of a coil. Obtain the expression for the energy stored in an inductor L connected across a source of emf.

Self-inductance of a coil is the property of the coil in which it opposes the change of current flowing through it.Self induction of long solenoid of inductance L, A long solenoid is one which length is very large as compared to its cross section area. the magnetic field inside such a solenoid is constant at any point and given byB=μ₀NI/lμ₀=absolute magnetic permeabilityN=total number of turnsMagnetic flux through each turn of solenoidΦ=B × area of each turnΦ=μ₀NI/l × Atotal flux=flux × total number of turnsNΦ=N(μ₀NI/l × A). (1)If L is the coefficient of inductance of solenoidNΦ=LI.. (2)from equation 1 and 2LI=N(μ₀NI/l × A)L=μ₀N²A/l(3)The magnitude of emf is given by|e| or e=LdI/dt.. (4)multiplying I to both sides eIdt=LIdI but I=dq/dtIdt=dqAlso work done (dW)= voltage X Charge(dq)or dW = eXdq = eIdtsubstituting the values in equation 4dW = LIdIBy integrating both sides∫₀ʷdW=∫₀ⁱ₀LIdI W=1/2LI₀²this work done is in increasing the current flow through inductor is stored as potential energy (U) in the magnetic field of inductorU=1/2LI₀²