Page 479 - Basic Electrical Engineering

5.2 MAGNETIC FIELD DUE TO CURRENT-CARRYING CONDUCTOR LAWS OF
ELECTROMAGNETISM

When a conductor carries current, a magnetic field is established around it in
a perpendicular plane in the form of concentric circles. The relationship

between the current, I and the magnetic field intensity, H is obtained by using
Amperes circuital law.

The magnetic field strength at a point due to an incremental length dl of
current-carrying conductors is determined by using Biot–Savart law. These
two laws are explained below.

5.2.1 Ampere’s Circuital Law

This law states that the line integral of magnetic field intensity, H around a

closed path is equal to the current enclosed by the path. Consider a current-
carrying conductor, I producing a magnetic field an a perpendicular plane as
shown in Fig. 5.6. The magnetic field intensity, H at a distance, r from the

current-carrying conductor is expressed as the line integral of H multiplied by
dl as equal to the total enclosed current. That is

If there are N number of current-carrying conductors enclosed then, H is
expressed as

where 2πr is the length of the flux path. This expression for H is the same as
in eq. (5.3).

5.2.2 Biot-Savart Law