VM170

VM170
Magnetic Field From a Square Current Loop

Overview

Reference:	W. B. Boast, Principles of Electric and Magnetic Fields, Harper & Brothers, New York, NY, 1948, pg. 199-200.
Analysis Type(s):	Coupled-field Analysis (ANTYPE = 0)
Element Type(s):	Coupled Thermal-Electric Line Elements (LINK68)
Input Listing:	vm170.dat

Test Case

A current, I, is carried in a square loop of side a. The space about the current is air. Determine the magnetic flux density at point P, at a height b above the current loop.

Figure 245: Square Current Loop Problem Sketch

Material Properties

Geometric Properties

μ_o = 4 π x 10^-7 H/m

ρ = 4.0 x 10^-8 ohm-m

a = 1.5 m

b = 0.35 m

I = 7.5 A

Analysis Assumptions and Modeling Notes

The problem requires a coupled electromagnetic field solution. LINK68 is used to create the current field in the wire loop. The current field established by the LINK68 elements is used to calculate the magnetic field at point P.

Nodes 1 and 5 overlap to create a closed current loop. The voltage at node 5 is set to zero while the current is applied to node 1.

The first solution calculates the current distribution in the loop. The BIOT command is then issued to calculate the magnetic field from the current distribution.

The cross-sectional area of the wire does not enter into the solution so an arbitrary area of 1.0 is input. Only one element is required per side of the square loop since the Biot-Savart integration of the magnetic field from the line element is exact. Flux density is calculated from the field intensity as B = µ_oH.

Results Comparison

Flux Density	Target	Mechanical APDL	Ratio
BX (x 10^-6 Tesla)	2.010	2.010	1.000
BY (x 10^-6 Tesla)	-0.662	-0.662	0.999
BZ (x 10^-6 Tesla)	2.010	2.010	1.000