3.2 Biot-Savart's Law

Soon after the qualitative study of magnetic effects of electric current, two French physicists Jean Baptiste Biot and Felix Savart performed qualitative study on the magnetic effect of electric current. They experimentally found that the magnetic effect at a point due to an electric current depends on the current strength, distance of the point from the current carrying conductor and geometry of the current carrying conductor. They stated their observations in the form of a law known as Biot-Savart's Law.

According to the Biot-Savart's law the magnitude of magnetic field dB at a point due to a current element ldl is directly proportional to

1.  the magnitude of current (I)
2. the length of current element (dl)
3. sine of the angle between the current element and the vector connecting the current element and the point  and
4. Inversely proportional to the square of the distance between them.

dB directly proportional to (Idl sin theta)/ r*r

or

The direction of magnetic field is perpendicular to the plane containing dl and r and is given by the right hand screw rule.

In the above expression muzero/4pie is the constant of proportionality and muzero is called the permeability of vaccum. Its value is 4piex 10 raised to -7 TmA raised to -1.

To represent a magnetic field the following convention is followed.

A magnetic field acting perpendicularly in to the plane of the paper is represented by the symbol o and a magnetic field acting perpendiularly out of the same of the paper is represented by the symbol dot.

The magnetic field at any point on the right of the conductor is into the plane of the paper and that on the left is out of the paper.

Biot-Savart law combined with the superposition principle is used to determine the magnetic field due to any current carrying conductor. In the following sections we shall obtain expressions for magnetic field due to a straight long conductor and also due to a circular coil carrying current using Biot-Savart law.

Magnetic Field due to a long
straight current carrying conductor

Introduction