Question

Biot Savart law full explanation​

Answer 1

Answer:

Biot-Savart law states that the magnetic field produced at a point near a current-carrying conductor is proportional to the material of the medium μ0, the current I flowing in the conductor, the small length of the wire dl

Biot-Savart law states that the magnetic field produced at a point near a current-carrying conductor is proportional to the material of the medium μ0, the current I flowing in the conductor, the small length of the wire dlinvolved, and inversely proportional to distance r between the point and the conductor.

Mathematically, dB∝μ0, dB∝I, dB∝dl and dB∝1r2

Then, dB=μ04π×Idlsinθr2, where θ is the angle betweendl

and r.

Now to find the intensity of the magnetic field at the center of a current-carrying circular loop, let the radius of the circular conductor be r. Let a constant current I flow through the loop, then

B=∫dB=μ04π×∫Idlsinθr2

Since the radius is always perpendicular to the tangent, we can say that dl

and r are perpendicular, θ=90∘, i.e. sinθ=1. Also the current I and radius r is a constant, we can take them out of the integral, then we get

B = integration dB = mew notI/4pier^2 x integration dl

We know that the total length of the circle, which is the perimeter is given as 2pr i.e.dl=2pr

Then B=µ0I4pr2×2pr

=µ0I2r

Hence the intensity of magnetic field B=µ0I2r

Additional information:

The Biot-Savart law was the basis of magnetostatics and gives the relationship between the current and the magnetic field for any shape of conductor. It is expanded from the ampere's circuital law.

Hope this helps.