Inductance of a Co-axial cable:-
Consider a coaxial cable with inner conductor having radius a and outer conductor of radius b and the current is flowing in the cable along z-axis in which the cable is placed such that the axis of rotation of the cable co-incides with z-axis.
the length of the co-axial cable be d meters.
we know that the between the region is
as , here the flux linkage
where -Total flux coming out of the surface
Since the magnetic flux will be radial plane extending from to and to .
Inductance of a Solenoid:-
Consider a Solenoid of N turns and let the current flowing inside it is ‘I’ Amperes. The length of the solenoid is ‘l’ meters and ‘A’ is its cross sectional area.
– Total flux coming out of solenoid.
, from the definition
As B is the Magnetic flux density given
from EQN(I) ,
The field strength H of a solenoid is
EQN (II) becomes
from the inductance definition
Inductance of a Toroid:-
Consider a toroidal ring with N-turns and carrying current I.
let the radius of the toroid be ‘R’ and the total flux emerging be
then flux linkage
the magnetic flux density inside a toroid is given by
where A is the cross sectional area of the toroid then
if the toroid has a height ‘h’ , inner radius and outer radius then its Inductance is Henries.