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Biot–Savart Law (Class 12 Physics – Magnetism)

The Biot–Savart Law gives the magnetic field produced at a point due to a small current element.

Formula:
B⃗ = (μ₀ / 4π) * (I · dl⃗ × r̂) / r²

Where:
B⃗ = Magnetic field at a point
μ₀ = Permeability of free space = 4π × 10⁻⁷ T·m/A
I = Current in the conductor
dl⃗ = Small length vector in direction of current
r⃗ = Position vector from current element to point of observation
r̂ = Unit vector in the direction of r⃗
r = Distance between the current element and the point
× = Vector cross product

Key Points:
Direction of B⃗ is given by the right-hand thumb rule.
Biot–Savart Law is analogous to Coulomb’s law in electrostatics.
It helps calculate magnetic field due to current-carrying wires, loops, and coils.

Special Case:
Magnetic field at the center of a circular loop:
B = (μ₀ I) / (2R)
Where R is the radius of the loop.