Biot-Savart Law

Biot-Savart’s Law and its Applications

Biot Savart's Law gives the field created by a current element that varies with the distance from the current element which can be used to describe magnetic fields by other current carrying conductors.

According to Biot Savart’s law, the magnitude of the magnetic field dB is proportional to the current i (more the current, more is magnetic field), the element length di, and inversely proportional to the square of the distance r (decreases with distance). Its direction is perpendicular to the plane containing dl and r. Thus in vector notation,

and is called permeability of free space.

(μ₀/4π is constant of proportionality.)

Direction of dB is given right hand thumb (if thumb points towards the direction of current, encircling of fingers givens direction of magnetic field).

S.I. unit is 1 tesla or 1T.

Note:

1.  is perpendicular to 
2. If q = 90^o then dB is maximum and minimum if q = 0^o or 180^o

Magnetic field due to a whole conductor is found by summing over all current elements.

Magnetic field bears resemblance with electric field in many ways. Firstly, both are long range forces that depend inversely on the distance between the source and field. Secondly, principle of superposition applies to both firlds.

It bears many differences also. Firstly, the field direction of magnetic field is perpendicular to radius, and that of electric field is along radius vector. Secondly, a scalar source (charge) produces electric field, while a vector source (current element) produces magnetic field.

Example Based on Biot-savart Law

Example:

An element ΔI = Δx i is placed at the origin and carries a large current I = 20 A. What is the magnetic field at the distance of 0.2 m. Δx = 1 cm.

Solution:

db = μ₀dl I × r/4π r³

dl = Δx = 10^-2m, I = 20A, r = 0.2m = y, μ₀/4π = 10^-7 Tm/A

θ = 90° : sinθ = 1

dB = 10^-7 * 20 * 10^-2 / 4 * 10^-2 = 5 * 10^-7 T