Define co-efficient of mutual induction and find an expression for it.

Explanation

Co-eficient of self-induction:

See Short Answer Type Question No. 2 (3 Marks) Self-inductance of a long solenoid Consider a long solenoid of length 4 area of cross-section A and number of turns per unit length n. Suppose that a current Iis passed through the solenoid. Then, magnetic field inside the solenoid is given by
`B = mu_(0) n I`
In case of long solenoid (length very large as compared to its radius), the magnetíc field produced well within the soenoid is practically constant. Therefore, the magnetic flux passing through each turm of the solenoid `= B xx` area of each turn
`=mu_(0) n I A` Total magnetic flux linked with the solenoid,
`phi` = gnetic flux linked with one `"turm"^(xx)` total number of turns
Now, total number of turns in the solenoid = n l
`therefore" "phi =mu_(0) n I A xx n I`
or `phi = mu_(0) n^(2) I A I" ....(i)"`
IfLis self-inductance of the solenoid, then
`phi = LI" ...(ii)"`
From equations (i) and (ii), we have
`L =mu_(0) n^(2) I A`
which is the required expression for coefficient of self induction.