Question

Drive Mathematiccal formula for Biot-Savert law.
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Answer 1

Biot Savart Law

Let a certain conductor be carrying a current ‘I’ in a direction .

Let ‘P’ be the point where the magnetic field due to the wire is situated.

Let a small portion be considered which is of length ‘dl’.

Let the line joining ‘dl’ and point ‘P’ from an angle θ with the tangent to ‘dl’.

• Here dB is the measurement of magnetic energy which arises from the electrical energy represented by I which act respectively as output and input.
• Therefore they should have direct dependency. i.e. dB ∝ I
• In a certain length of a conductor, certain amount of charge is present at a moment and the magnetic effect it can produce depend on the total number of charges, which in turn depend on the length consider, i.e. dB ∝ dl.
• Any force or phenomena which spread out spherically have inverse proportionality to the square of the distance between the source and point of observation. dB ∝ $\dfrac{1}{{r}^{2}}$
• Similarly the magnetic field is found to be least when the angle between r and dl is the smallest 0° and it is largest when the angle is 90°.
• So, dB ∝ sin $\theta$

Thus , we have,

$dB = \dfrac{ {\mu}_{0}}{4\pi} \frac{Idl \sin \theta }{ {r}^{2} }$