Magnetic Field Due To A Thin Straight Wire

Consider an infinitely long, thin, straight current carrying wire. The magnetic field created by the current in its proximity can be calculated using the Biot-Savart law.  

To estimate the magnetic field at a point P, consider a small current element of length “dx”, at a distance “x” from the origin. The length of the line joining “dx” and “P” can be estimated using the Pythagorean theorem.

The angle subtended by the current element with the line joining P can be expressed as a over r.  

Substituting these terms gives the expression for the magnetic field created by the current element.

Since the wire is infinitely long, the total field is found by integrating from negative infinity to infinity. Because this integral is an even function, the calculation is simplified by integrating from zero to infinity and doubling the result. This integration gives the total magnetic field at point P.

Following the right-hand rule, if the thumb points along the current direction, then the fingers curl along the direction of the magnetic field lines. These concentric lines weaken with distance, increasing the space between them.