Question

applications of biot savarts law​

Answer 1

Answer:

to find magnetic field.........

Answer 2

i) Magnetic Field due to steady current in an infinitely long straight wire

Consider a straight infinitely long wire carrying a steady current I

We want to calculate magnetic field at a point P at a distance R from the wire as shown below in figure From Biot,-Savart law ,magnetic field dB due to small current element of the wire at point O at a distance |r|=r from point P is

since current element Idl and vector r makes an angle θ with each other ,the magnitude of the product dlXr is dlrsinθ and is directed perpendicular to both dl and r vector as shown in the figure Since from our choice of co-ordinate, we found out that field B lies along z-axis therefore we can write

where k is the unit vector along z-axis

we will now express sinθ and r in terms of R which is fixed distance for any point in space and l which describes the position of current element on the infinitely long wire .From figure 1 we have

and r=(R2 +l2)1/2

Putting these values in the equation (5) we find

To find the field due to entire straight wire carrying wire ,we would have to integrate equation (6) B=∫dB

To evaluate the integral on the RHS substitute

l=RtanΦ and dl=Rsec2Φ dΦ

Therefore