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प्रश्न
Explain Biot Savart's Law.
Explain Biot and Savart’s law with suitable diagram.
उत्तर
Statement of Biot Savart's Law: The magnitude of magnetic induction (dB) 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`
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