The document discusses different topics related to inductance including: 1) Self-inductance is defined as the ratio of the total flux linkage to the current through a solenoid or coil. 2) The flux density of a toroid coil is proportional to the current through it and inversely proportional to its radius. 3) Mutual inductance is defined as the ability of one coil to produce an emf in a nearby coil when the current in the first coil changes, and is proportional to the flux from the first coil that is coupled to the second coil.

1. Indoctor

2. Inductance
Consider a solenoid of N turns in which current I produce a total flux of
If each of the N turns links with the total flux ‘ ‘ then the flux linkage is ‘ ‘
We can define self inductance as the ratio of the total flux linkage, to the current
through it
H on the axis of the solenoid
Self inductance
Self inductance

3. Inductance of Toroid
Consider a Toroid of N turns with radius of ‘R’ and it carries current ‘I’
The flux density of the coil

4. Mutual Inductance
Change in the flux of one coil induce ‘emf ’ in the other coil
Mutual inductance is defined as a ability of one coil to produce an ‘ emf ’ in a
near by coil, when the current in the first coil change
Out of the flux only flux alone is coupled to the second coil.
The mutual inductance due to coil 1 on coil 2
Out of the flux only flux alone is coupled to the second coil.
The mutual inductance due to coil 2 on coil 1
Due to distance is constant

6. Apply the KVL in a closed loop
Multiply by i on both side
Power Supplied = Power dissipated + Power Stored
Energy Density in Magnetic field

7. Multiply both denominator and Numerator by

8. Boundary condition for Magnetic Field
Boundary between the different material
For tangential component
We know that
The normal component become negligible when
Thus Magnetic filed intensity is continuous across the boundary
Thus Magnetic flux density is discontinuous across the boundary
If the boundary is current free region i.e. I = 0

9. Normal Component
Gauss’s Law for Magnetic field
When , the flux crossing the sides become zero
Thus Magnetic flux density is continuous across the boundary
Thus Magnetic field intensity is discontinuous across the boundary