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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