Biot-Savart Law: Magnetic Field Calculation

Biot-Savart Law

• Magnetic field at point 'P' due to a current element 'i dl' is given by the expression: dB = μ₀ i dl sin θ / 4π r²
• In C.G.S. units, k = 1, so dB = i dl sin θ / r² Gauss
• In S.I. units, k = μ₀ / 4π, so dB = μ₀ i dl sin θ / 4π r² Tesla
• μ₀ is the absolute permeability of air or vacuum, approximately 4π × 10⁻⁷

Magnetic Field and Current

• A magnetic field is established around a current-carrying conductor
• Magnetic field exists as long as there is current in the wire
• The direction of the magnetic field is reversed when the direction of current is reversed

Current Element

• Current element is the product of current and length of an infinitesimal segment of a current-carrying wire
• Current element is a vector quantity with the same direction as the current
• Current element AB = i dl

Biot-Savart's Law and Coulomb's Law

• Both laws relate to the inverse square of the distance from the source
• The current element produces a magnetic field, while a point charge produces an electric field
• The magnetic field created by a current element is perpendicular to both the length element dl and the unit vector r̂

Direction of Magnetic Field

• Determined using Maxwell's cork screw rule
• If a right-handed screw is placed along the current-carrying linear conductor and rotated in the direction of current flow, the direction of rotation of the thumb gives the direction of magnetic lines of force