Question

explain Biot Savart law write expression for magnetic field due to infinitely long current carrying conductor and circular evil carrying current at its Centre write direction of magnetic field in both cones

Answer 1

Electric fields and magnetic fields might seem different, but they're actually part of one larger force called the electromagnetic force. Charges that aren't moving produce electric fields. But when those charges do move, they instead create magnetic fields. For example, a magnet is only a magnet because of moving charges inside it. And charges moving in an electric wire also produce magnetic fields. If you move a compass near to an electric wire, you'll find that the compass needle changes direction.

The Biot-Savart Law is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points.

To derive this law, we first take this equation for electric field. This is the full version, where we use muu-zeroover 4pi instead of the electrostatic constant k. Since we're looking at a wire, we replace the charge q with I dl, which is the current in the wire, multiplied by a length element in the wire. Basically it's treating this little chunk of the wire as our charge. And we also replace the electric field E with a magnetic field element dB because a moving charge produces a magnetic field, not an electric field.

Last of all, we have to realize that a current has a direction (unlike a charge). So we need to make sure the direction of the current affects our result. We do that by adding sine of the angle between the current and the radius. That way, if the wire is curvy, we'll take that into account. And that's it - that's the Biot-Savart law.