Biot-Savart Law



The Biot-Savart Law relates magnetic fields to the currents which are their sources. In a similar manner, Coulomb’s law relates electric fields to the point charges which are their sources. Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculus problem when the distance from the current to the field point is continuously changing.

Biot-Savart Law

 

Consider a conductor through which a current I flows and let small elemental length dl at a source point. We want to calculate magnetic field at a point which is distance r from source point. θ be the angle between r and dl. Then from biot-savart law the magnetic field due to current carrying conductor is

directly proportional to the magnitude of current

Biot-Savart Law

 

directly proportional to the length of element dl

 

Biot-Savart Law

 

directly proportional to the sine of angle between r and dl

 

Biot-Savart Law

 

inversely proportional to the square of the distance between source point and field point

 

Biot-Savart Law

 

Now from above equations we get,

 

Biot-Savart Law

 

Hence total magnetic field due to current carrying conductor is

 

 

 

Biot-Savart Law

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