Express Biot – Savart law in the vector form.

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#### Solution

Consider a straight infinnitely long wire carrying a steady current I. Point P is the perpenicular distance from the wire. Consider a small element dl of the wire at the point O on the wire. The line joining points O to P( OP = vector r ) makes an angle θ with the direction of the current element dl.

`dvecB = (μ_oI)/(4π) (vec(dl) xx vec r)/r^3`

The expression for the total magnetic field B due to the wire can be obtained by intergrating the above expression as

`vecB =∫(μ_oI)/(4π) (vec(dl)xxvecr)/r^3`

It is the biot savart law which gives the magnetic field B generated by steady electric current I when the current can be approximated as running through an infinitely running wire.

Concept: Magnetic Field Due to a Current Element, Biot-Savart Law

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