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----> ampere's law :

which is to be used while finding magnetic fields inside the enclosed surface. we are allowed to use it to any surface however the surface have to be in such ways that the path must pass through the point and the path must have enough symmetry so that is constant along the large path of it!

----> Biot Savart law : we often use biot savart to find magnetic fields

generated by an electric current carrying wire of radius "r" and since the radius is perpendicular with I we don't worry about messy integration!

thus we left with : dB =( µ_0 Idl) / (4πr^2)

also knowing that l = 2πr helps so we substitute it in! and we eventually end up with : dB =( µ_0 Id2πr) /(4πr^2)

Thus B = µ_0 I / 2πr

Combining Ampere Law to Biot savart.

Thus we can derive Biot savart from ampere by the following:

§ B.dl = µ_0 I (encl)

B § dl = µ_0 I (encl) hence B (2πr) is

B(2πr) = µ_0 I

so B = (µ_0 I) / 2πr

faith nshuti.

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Q: Derivation of amperes law from biot savart law?
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