Calculate magnetic field strength around a bus bar?

[LaSalle1940]

I'm sure this is well-established but I don't know the appropriate reference. Anyhow: I need to calculate the magnetic field strength around a bus bar at various distances from that bar. We can assume that we know, going in, the current, the voltage, the dimensions of the bar, and the nature of the material of the bus bar. I'm sure there's a (relatively [?]) simple relation to give the field strength in gauss at some radius (?) from the center of the bar, and it's that equation--and an appropriate reference in which it appears--that I need to know. Thanks.

 

[jghrist]

If you are far enough away that the current could be considered uniform radially from the center of the bus, then the flux density is

B = 2·10^-7·I/r webers/m²

where I is the current in amperes and r is the distance from the center of the bus in meters.

Electrical Engineering Science, Clement & Johnson, McGraw-Hill, 1960, p. 63.

 

[LaSalle1940]

OK, that gives rise to a couple more questions:

* What is the effect of bus bar geometry? That is, the bus bar in question is rectangular in cross-section.
* I'm not sure what constitutes being sufficiently far away that the current criterion you describe is met.
* Concerning terminology and units: am I correct that "flux density" is the same as magnetic field strength, and that webers/m² is the same as gauss?

Thanks.

 

[desertfox]

Hi LaSalle

The Magnetic intensity H has units of = amps/m.
The magnetic flux density B has units of= webers/m^2.
Therefore they are not the same. However they are related by the formula :-

B=[μ]o H

where [μ]o = permeability of free space or magnetic
constant

The only formula I have is similar to that in the previous post except my formula uses H ie:-

H= 2*I/d

for a field at a perpendicular distance d from the wire.

This formula is for a long (straight wire only) carrying a current.
I believe the shape of the conductor would have influence on the field and also the material of which the busbar is made from.

regards desertfox

 

[Skogsgurra]

The Biot-Savart law (applied to an infinitely long, thin and straight conductor) states that B = (I*4*PI*10^-7)/R, where I is the current in A, R is the distance in metres and B is the field strength in Tesla. If you plug in 1 A and 1 m, you get 0.2 microtesla.

A set of bus bars that carry three phase current will have a net current equal to zero and the field a few metres away will be zero. It is only when the conductors are separated from each other that you get a net field. You can calculate the field from each conductor and add them to get the resulting field (superposition valid). Do not forget to include the phase angles.