Indoctor

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

Inductance of Toroid

Consider a Toroid of N turns with radius of ‘R’ and it carries current ‘I’

The flux density of the coil

Mutual InductanceChange 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

Apply the KVL in a closed loop

Multiply by i on both side

Power Supplied = Power dissipated + Power Stored

Energy Density in Magnetic field

Multiply both denominator and Numerator by

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

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