What is self-inductance of a coil ? Write its SI U Unit.
Obtain the expression for energy stored in an inductor.

Explanation

Self inductance of a coil is numerically equal to the emf induced in the coil due to unit rate of change of current in it. The SI unit of self inductance in henry (H).
Let dw be the work done to establish a current I in the coil in a time dt.
Then `(dw)/(dt)=|epsilon|I " " epsilon` is the induced emf
since `epsilon=-L (dI)/(dt)`
`(dw)/(dt)=L(dI)/(dt)I`
`dw=L(dI)/(canceldt)canceldtI`
dw=LI dI
The total work done in establishing the current is ,
`W=int dw=int_0^I L I dI =L[I^2/2]_0^1`
`W=1/2LI^2`
Thus the magnetic P.E. stored in an inductor of self inductance L carrying a current I is
`W=1/2LI^2`