Question

write biot-Savarts law?????????????​

Answer 1

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A current element is a conductor carrying current.It is the product of current,I and length of very small segment of current carrying wire ,dL.

Let us consider a small element AB of length dl of the conductor RS carrying a current I.

Let r be the position vector of the point P from the current element I dL.and θ be the angle dl and r.

According to Biot-Savarts law,the magnetic field induction dB or magnetic flux density at a point P due to current element depends upon the following factors.

(i) dBI

(ii) dBdl

(iii) dBsinθ

(iv) dB1/r^2

Combining these factors,we get

dBIdLsinθ/r^2

or dB=K Idl sinθ/r^2

where K is a constant of perportionality.

In S.I units, K=μ0/4

thus , dB=μ0/4 I dl sinθ/r^2

where μ0 is absolute premeability of free space and

μ0=4*10^-7 Wb A^-1m^-1

= 4*10^-7*TA^-1m [ 1T=1 Wb m^-2]

In C.G.S units,K=1 (In free space)

Thus dB=Idl sinθ/r^2

In vector form,

dB=μ0/4 I(dl*r)/r^3

magnetic field induction at point P due to current through entire wire is

B=∫μ0/4Idl*r/r^3

Or B=∫μ0/4 Idl sin θ/r^2

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Answer 2

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Biot Savart Law

• Directly proportional to current (I)

• Directly proportional to the length of the element (dl)

• Directly proportional to the sine of angle θ between the direction of current and the line joining the element dl from point A.

• Inversely proportional to the square of the distance (x) of point A from the element dl.