Abstract: The distribution of magnetic field in space and Ampere forces on conductors

with different cross - section shapes are of great significance in practical engineering

applications.In this paper，the magnetic field distri-bution of the current-carrying conductor with infinite rectangular cross-section and circular

cross-section is theoret- ically analyzed and calculated，and then the Ampere Forces between

two parallel rectangular cross-section conduc- tors and between two circular cross-section

ones are analyzed，the magnetic field distribution and Ampere force are

simulated by Matlab software.The results show that the magnetic induction lines of the

current-carrying conductors with rectangular cross-section are nearly elliptic，and the Ampere

force between the two parallel rectangular cross- section current-carrying conductors is not

only related to the distance and cross-section size，when the distance and cross-section size are

fixed，it also depends on the direction of placement. When the side length ratio a / b >

1，the Ampere Force is less than that of two circular cross-section conductors with the same area and

current-carrying den- sity.And the smaller the a / b values，the greater the force is.When a / b

<1，the force is greater than that.But with the increase of conductor spacing，the difference of two forces becomes smaller and smaller.

Key words: rectangular cross-section conductor, circular cross-section conductor, magnetic field, Ampere force