Question

show that magnetic energy required to build current in coil of self inductance is given bye 1/2 LI2

Answer 1

Self -Inductance is the property by which an opposing induced emf is produced in a coil due to a change in current, or magnetic flux, linked with the coil.

OR

Self-inductance of a coil is numerically equal to the flux linked with the coil when the current through the coil is 1 A.

OR

Self-inductance of a coil is equal to the induced emf developed in the coil when the rate of change of current in the coil is one ampere per second.  

Energy stored in an inductor :

Consider a source of emf connected to an inductor L. As the current starts growing, the opposing induced emf is given by