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Application of Biot-Savart law, field due to circular loop
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Application of Biot- Savart Law This law is used to determine the magnetic fields in space due to any current carrying conductor. This Law is used to determine the force between two long and parallel current carry conductors. This law is also used to calculate the Magnetic field on the axis of a c...

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  • August 23, 2022
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  • 2021/2022
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  • biot savart law
  • physics

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  • Secondary school
  • Physics
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Biot-Savart Law and its application to circular current loop:


Let us consider a current element of length dL carrying current I through it. There is a point P at
distance r from current element and ɵ is the angle between dL and r.




Biot-Savart Law:

The Biot-Savart law is used to determine magnetic field(dB) at a given point, due to a current
element (current carrying conductor) and states that, magnetic field at a point due to a current
element is;
(i) directly proportional to the amount of current(I) through conductor wire, i.e.
dB ∝ I --------------(i)
(ii) directly proportional to the length(dL) of the current element, i.e
dB ∝ dL ------------(ii)
(iii) inversely proportional to square of the distance(r) of reference point from current
element, i.e.
dB ∝ 1/r2 -----------(iii)
(iv) directly proportional to the angle(ɵ) between current element(dL) and position
vector(r), i.e.
dB ∝ sinɵ ------------(iv)

Combining all above equations we get,

dB ∝ I dL sinɵ/r2

or dB = k I dL sinɵ/r2

(Here k is proportionality constant and in S.I. unit its value is [µo/4π] = 10-7 T m A-1).

Thus finally we get,

dB = (µo/4π ) (I dL sinɵ)/r2 -------------(v)

This equation is the mathematical form of Biot-Savart law.

Total magnetic field due to the whole wire cab be determined by integrating equation (v) over
the length of wire.

In vector form Biot-Savart law(v) can be written as;

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