Question

Express the Biot-Savart law in vector form.

Answer the following question briefly and to the point:

Write Biot-Savart’s law in vector form.

Answer 1

Consider a straight, infinitely long wire carrying a steady current I. Point P is the perpendicular 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.

`d vec B = (μ_o I)/(4 pi) (vec(dl) xx vec r)/r^3`

The expression for the total magnetic field B due to the wire can be obtained by integrating the above expression as
`vec B = int(μ_o I)/(4 pi) (vec(dl) xx vec r)/r^3`
It is the Biot-Savart law that gives the magnetic field B generated by a steady electric current I when the current can be approximated as running through an infinitely long wire.

Answer 2

Biot-Savart’s law in vector form,

`d vec B = mu_0/(4 pi) (I (d vec l xx vec r)/r^3`

(Magnetic field at a distance r from a current element dl).