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Using Ampere 's circuital law or Biot- S...

Using Ampere 's circuital law or Biot- Savart's a law, show that magnetic flux density B at point P at a perpendicular distance a from a long current carrying conductor is given by `B=(mu/(4 pi))(2I)/(a)` [ Statement of the laws not required]

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Let XY be a long straight wire carrying current I.
Let .P. is a point at a distance .a. from the wire
where magnetic field is to be found.

Let us consider a circle element dl at P.
`ointvecB.vec(dl)=ointB.dl`
`=Bointdl`
Since B is constant around the circle.
`ointdl=2pia`
`ointvecB.vec(dl)=Bxx2pia`
From Ampere.s circuital law,
`ointvecB.vec(dl)=mu_(0)I`
`:.Bxx2pia=mu_(0)I`
or `B=(mu_(0)I)/(2pia)`
or `B=((mu_(0))/(4pi))(2I)/(a)`
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