Magnetic Field Due To A Current Element Biot Savart Law

When a current flows through a wire, it generates a magnetic field around it. The direction of the magnetic field is determined by the right-hand rule, which states:
- If you hold the wire with your right hand such that your thumb points in the direction of the current, your fingers curl in the direction of the magnetic field. Since the current is flowing upward, the magnetic field lines will circulate anti-clockwise when viewed from above.
The strength of the magnetic field is proportional to the distance from the wire. Using Ampere’s Law, we know that the magnetic field strength ( ) around a straight conductor decreases with the increase in distance from the wire: Where:
- is the magnetic field strength,
- is the permeability of free space,
- is the current,
- is the radial distance from the wire.
Thus, the magnetic field strength at point A, which is closer to the wire, will be greater than the magnetic field strength at point B, which is farther from the wire.
Thus, the magnetic field lines are anti-clockwise, and the magnetic field strength at A is more than at B.

Given that there are two straight wires carrying current at a 90° angle, the magnetic field at point will be the vector sum of the magnetic fields due to each of the wires. The magnetic field at a point due to a straight current-carrying wire is given by: where is the distance from the wire to the point of interest. For each wire, the magnetic field will have different directions, but since the currents are of equal magnitude and the angle between the wires is 90°, the fields from both wires will cancel each other out at point . Therefore, the net magnetic field at point is: Thus, the net magnetic field at point P is zero.