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Magnetic Flux Density Due to a Current Carrying Conductor
Whenever a electric current passes through a conductor, a magnetic field is appeared surrounding it. The direction of this magnetic field of electric current carrying conductor can be determined by Cork Screw rule or Right Hand rule.
As per Biot Savart’s law, the expression of magnetic flux density at a point P nearer to a conductor carrying a electric current ‘I’ is given as,
Where, dB is the infinitesimal flux density at point P.
Current I is passing through the conductor.
dl is infinitesimal length of conductor.
r is the radius vector from center of element dl to point P.
θ is the angle between electric current and radius vector.
Flux Density due to Current Carrying Conductor
Now in order to find the actual magnetic flux density B at the point P due to total length of the conductor, we have to integrate the expression of dB, in respect of dl.
The above expression is used to evaluate magnetic flux density B at any point due to infinitely long linear conductor and this comes as
Here, R is the radial distance from conductor to the point P.
Now if we integrate B around a path of radius R enclosing the electric current carrying conductor, we get
This equation shows that the integral of H around a closed path is equal to the current enclosed by the path. This is nothing but Ampere’s law. If the path of integration enclosed N number of turns of wire, each with a electric current I in the same direction, then
This relation is very important relation; it is used for determining flux linkage of a system of conductors. From flux linkage, the inductor of the system can easily be determined.
If the electric current in the conductor varies, it causes variation of flux linkage. We know that change of flux linkage induces a voltage in the conductors and the rate of change of flux linkage is directly proportional to the induced voltage. This is known as Faraday’s laws of electromagnetic induction.
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