BIOT-SAVART’S LAW DERIVATION
BIOT-SAVART’S LAW OR AMPERE’S LAW FOR CURRENT ELEMENT
Biot-Savart’s law deals with the magnetic field induction at a point due to a small current element.
A current element is a conductor carrying current.It is the product of current,I and length of very small segment of current carrying wire ,dL.
Let us consider a small element AB of length dl of the conductor RS carrying a current I.
Let r be the position vector of the point P from the current element I dL.and θ be the angle dl and r.
According to Biot-Savart’s law,the magnetic field induction dB or magnetic flux density at a point P due to current element depends upon the following factors.
Combining these factors,we get
or dB=K Idl sinθ/r2
where K is a constant of perportionality.
In S.I units, K=μ0/4π
thus , dB=μ0/4π I dl sinθ/r2
where μ0 is absolute premeability of free space and
μ0=4π*10-7 Wb A-1m-1
= 4π*10-7*TA-1m [ 1T=1 Wb m-2]
In C.G.S units,K=1 (In free space)
Thus dB=Idl sinθ/r2
In vector form,
magnetic field induction at point P due to current through entire wire is
Or B=∫μ0/4π Idl sin θ/r2
BiotSavart’s law in terms of magnetising force or magnetic intensity (H) of the magnetic field:
In S.I System,
dH=dB/μ0=1/4π Idl*r/r3=1/4π Idl*αr/r2
H= ∫1/4π Idl sinθ/r2
Importance OF BIOT SAVART’S LAW:-
- This law is analogous to Coulomb’s law in electrostatics.
- Biot Savart’s law is valid for a symmetrical current distribution.
- This law cannot be easily verified experimentally as the current carrying conductor of very small length cannot be obtained pratically.
- Biot Sarvart’s law is applicable only to very small length conductor carrying current.
- The direction of dB is perpendicular to both Idl and r.