Biot - Savart Law || Class 12 - Moving Charge and Magnetism - 8 || in HINDI

In this Physics video lecture in Hindi for class 12 we explained Biot Savart Law and did the derivation of the formula of its scalar as well as its vector form.
Class 12 - Moving Charge and Magnetism - Part 8
Consider a current I is flowing through a conductor XY. Due to the flow of current magnetic field is produced around the wire. Let us consider an elementary portion of length dl and point P is r distance from that elementary portion.
Biot and Savart found that the magnetic field at point P due to the elementary portion of the wire is,
Directly proportional to the current, i.e.,
dB ∝ I .
Directly proportional to the length of the wire, i.e.,
dB ∝ dl.
Directly proportional to the sine of angle between the direction of flow of current and line
joining the elementary portion and the point P, i.e.,
dB ∝ sine θ.
Inversely proportional to the square of the distance of the point P from the elementary portion, i.e.,
dB ∝ 1/r^2
Considering all the factors, we have
dB ∝ (I dl sine θ)/r^2
or, dB = k (I dl sine θ)/r^2
where, k is constant of proportionality.
In vacuum,
k = μ_0/4π = 〖10〗^(-7) T A^(-1) m
where, μ_0 is called absolute permeability.
Therefore, in S.I., Biot-Savart’s law can be expressed as
dB = μ_0/4π (I dl sine θ)/r^2
Direction of dB ⃗ :- the direction of this magnetic field is same as the direction of the vector dl ⃗ × r ⃗. It follows that the direction is perpendicular to the plane of the paper and directed inwards.
Hence in vector notation,
dB ⃗ = μ_0/4π (I dl ⃗ × r ̂ )/r^2 = μ_0/4π (I dl ⃗ × r ⃗ )/r^3