# Magnetic Field of Current Carrying Conductor

A wire carrying an electric current generates a magnetic field around it, due to the magnetic fields generated by the individual charges moving within the conductor. The magnetic fields of the individual charges can be described mathematically as a series of planar concentric circles, as shown above, oriented at right angles to the direction of motion of the charged particle. The magnetic fields generated by the individual charges add together to produce a cylindrical magnetic field surrounding a linear conductor, such as a wire. The direction of the magnetic field is given by the right-hand rule and is clockwise for a conventional current directed into the page.
The intensity of the magnetic field surrounding a current-carrying conductor is directly proportional to the current, as it is the sum of the magnetic fields generated by the charged particles moving within the conductor, and inversely proportional to the distance from the conductor.
The magnetic fields of the individual charges moving within the conductor are planar and circular. If we let B represent the magnetic field due to a single moving charge, at a distance d from the conductor, the field to this moving charge will be distributed over a circle of the circumference of 2$\pi$d, and have intensity (strength) of B/2$\pi$d at any point on a circle of radius d, which is oriented at right angles to the direction of motion of the charge and centered on the moving charge. At a distance of 2d from the conductor, the intensity of the magnetic field will be B/4$\pi$d at any point on a circle of radius 2d, which is oriented at right angles to the direction of motion of the charge and centered on the moving charge.
Fig.no.1: Circular distance from a point charge.
The magnetic field strength due to a current-carrying conductor is given by the equation: $$B = k {I \over d}$$ where: B = Magnetic field strength(T).
k = The Magnetic force constant.
I = Current.
d = Distance(m).