Lastly, magnetic field density at that point P due to that infinitesimal portion of the wire is also directly proportional to the actual length of the infinitesimal length dl of wire. It is also very natural to think that the magnetic field density at that point P due to that infinitesimal length dl of wire is inversely proportional to the square of the straight distance from point P to the center of dl. If you try to visualize the condition, you can easily understand the magnetic field density at point P due to that the infinitesimal length dl of the wire is directly proportional to the current carried by this portion of the wire.Īs the current through that infinitesimal length of wire is the same as the current carried by the whole wire itself, we can write, Here, r is a distance-vector that makes an angle θ with the direction of current in the infinitesimal portion of the wire.

Let us also consider an infinitely small length of the wire dl at a distance r from the point P as shown. The wire is presented in the picture below, in red color. Let us consider a long wire carrying a current I and also consider a point p in the space. Therefore, the final Biot Savart law derivation is, Where, k is a constant, depending upon the magnetic properties of the medium and system of the units employed. Through observations and calculations, they had derived a mathematical expression, which shows, the magnetic flux density of which dB, is directly proportional to the length of the element dl, the current I, the sine of the angle, and θ between the direction of the current and the vector joining a given point of the field and the current element and is inversely proportional to the square of the distance of the given point from the current element, r. Viewing the deflection of a magnetic compass needle, these two scientists concluded that any current element projects a magnetic field into the space around it. The Biot Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb’s law in electrostatics.īiot Savart law was created by two French physicists, Jean Baptiste Biot and Felix Savart derived the mathematical expression for magnetic flux density at a point due to a nearby current-carrying conductor, in 1820. Biot–Savart law is consistent with both Ampere’s circuital law and Gauss’s theorem. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot-Savart Law is an equation describing the magnetic field generated by a constant electric current.

Biot savart law