Electrical Engineering ⇒ Topic : Amperes Work Law or Amperes Circuital Law

Ampere's Work Law or Ampere's Circuital Law

The magnetising force (H) at any point in an electromagnetic field is the force experienced  by a unit N-pole placed at that point. If the unit N-pole is made to move in a complete path around N current-carrying conductors, then work is done provided the unit N-pole is moved in opposition to the lines of force. Conversely, if the unit N-pole moves in the direction of magnetic field, then work will be done by the magnetic force on whatever force is restraining the movement of the pole. In either case, unit N-pole makes one complete loop around the N conductors. The work done is given by Ampere's work law stated below :

The work done on or by a unit N-pole in moving once around any complete path is equal to the product of current and number of turns enclosed by that path i.e.

                                                                             figure (a)

where H_r is the magnetising force at a distance r. The circle around the integral sign indicates that the integral is around a complete path.

The work law is applicable regardless of the shape of complete path. Thus in Fig. (a), paths 'a' and `b' completely enclose N conductors. If a unit N-pole is moved once around any of these complete paths, the work done in each case will be equal to NI. Although path 'c' is a complete path, it fails to enclose any cun-ent carrying conductor. Hence, no work is done in moving a unit N-pole around such a path.

Note. The work law is applicable for all magnet c fields, irrespective of the shape of the field or of the materials which may be present.

AMPERE'S CIRCUIT LAW

Consider a closed current system C₁ carrying a current of I A. The magnetic flux lines of the system are shown in Fig. 1 (a). Let Φ₂ be another such magnetic flux line linking C₁. The direction of H is shown to be tangential to the flux line Φ₂. Let P be a point on the flux line . Let dl be the elementary length around P measured in the direction of the flux line. Then, according to Ampere's circuit law, the line integral

                            .............. (1)

In the circuit shown in Fig. 1 (a), any flux line Φ₂ is linking only once with C₁. Thus, applying this law to the circuit in Fig. 1 (b), we get

                            FIGURE (1) Ampere's circuit law

This is due to the fact that the flux line Φ₂ is linking the current three times. If the coil has N turns, then

The product NI on the right hand side is known as the magneto-motive force (mmf).