Question

Explain Biot Savart's Law.

Explain Biot and Savart’s law with a suitable diagram.

Answer 1

Statement of Biot Savart’s Law: The magnitude of magnetic induction `(dvecB)` at a point due to a small element of current carrying conductor is directly proportional to the current, directly proportional to the length of the element, directly proportional to the sine of the angle between the element and the line joining the center of the element to the point and inversely proportional to the square of the distance of the point from the center of the element, i.e., `dB prop (Idl sin theta)/r^2`.

Explanation:

Consider a small element of length d l of conductor carrying current I.

Let P be any point at distance ‘r’ from the conductor.

Let θ be the angle between dl and r.

dl - Length of element along the wire

Let dB be the magnetic induction at point P.

By Biot-Savart law,

`dB prop (Idl sin theta)/r^2`

`dB = K (Idl sin theta)/r^2`,

where K is constant and `K = mu_0/(4 pi)`

∴ `dB = mu_0/(4 pi) (Idl sin theta)/r^2`

In vector form,

`dvecB = mu_0/(4 pi) (Ivec(dl) xx vecr)/r^3`