ELECTRICAL METHODS 



581 



Ampere's haw 



The magnitude or strength of the magnetic field surrounding a cur- 

 rent-carrying conductor may be obtained from Ampere's law. This law 

 describes the magnetic field due to a conductor element of length dl at an 

 external point P. Referring to Figure 362, the field at F is : 



jTj — idlsmd ... 



where r^ 



dH — magnetic field 

 /= current 



dl = length of current element 

 r = distance between dl and P 

 6 = angle between dl and r 



Furthermore, the magnetic field is perpendicular to the plane determined 

 by r and dl. 



Fig. 362. — Sketch illustrating geometric rela- 

 tion between field dH at P and current I flow- 

 ing in current element of length dl. (From 

 Ampere's law dH is perpendicular to the plane 

 formed by dl and r.) 



Fig. 363. — Sketch illustrating 

 the geometric relations between 

 the quantities I, dl, etc., which 

 enter into the computation of the 

 magnetic field at a point P. 



Ampere's law governs the magnetic field of direct current and alter- 

 nating current. If the current flowing in the conductor is an alternating 

 current, the magnetic field surrounding the conductor is an alternating 

 field which has the same frequency as the current, and is in phase with it. 



Equation 1 may be used to determine the resultant or total magnetic 

 field due to a current flowing in any conductor or group of conductors, 

 provided the integration with respect to / and r can be carried out. In 

 particular, Equation 1 may be applied, in a rather simple manner, for 

 determining the magnetic field produced by a linear flow of current. Refer- 

 ring to Figure 363, it is desired to calculate the magnetic field H at a point P 

 due to the current I flowing in the direction indicated. From Equation 1 

 the field due to an element of conductor of length dl is 



jjj I dl sin 6 

 dH = = 



