Question

biot savarts law explain it​

Answer 1

Biot savart 's law is used to determine the strength of magnetic field at any point due to currenr carrying conductor.

Derivation-

Consider

• a very small element AB of length dl,

• Current passing through it,

• strength of magnetic field db due to samll current element dl at point p,

• r is the distance.

(Refer the attachment for figure)

Strength of Magnetic field is directly proportional to small current element, current and the angle between dl and r and also it is inversly proportional to the distance between point p and current element.

so ,

• $\bf{db \propto dl}$

• $\bf{db \propto I}$

• $\bf{db \propto sin \theta }$

where $\theta$ is the angle between dl and r

• $\bf{db \propto \dfrac{1}{r^2 }}$

now combining all we get,

$\bf{db \propto \dfrac {I dl sin \theta }{ r^2} }$

$\bf{db = k \dfrac {I dl sin \theta }{ r^2} }$

where k= constant  = absolute permeability

$\sf { k= \dfrac{\mu_o}{4 \pi } }$

$\boxed{\bf{\pink{db = \dfrac{\mu_o}{4\pi } .\dfrac {I dl sin \theta }{ r^2} }}}$

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Answer 2

$\underline{ \tt{Biot \: savart's \: law}}$

Biot savart's law states that magnetic field at point A due to current flowing through a small element is

• Directly proportional to the current

• Directly proportional to the length of the element

• Directly proportional to sine of angle b/w the direction of current and the line joining the element from point

• Inversely proportional to the square of distance of point A from element

Mathematically ,

$\implies \tt {B \propto \frac{Idl \sin( \theta) }{ {(r)}^{2} } }$

$\implies \tt {B = k\frac{Idl \sin( \theta) }{ {(r)}^{2} }}$

Where ,

• I = current
• dl = length of element
• k = 10^(-7) T-m/Amp

Magnetic field is minimum , Φ = 0°

Magnetic field is maximum , Φ = 90°