VM49

VM49
Electrostatic Field Analysis of Quadpole Wires

Overview

Reference:

Any Basic Static and Dynamic Electricity Book

Analysis Type(s):

Static, Electrostatic Analysis (ANTYPE = 0)

Element Type(s):

2D 8-Node Electrostatic Solid Element (PLANE121)

2D Infinite Solid Element (INFIN110)

Input Listing:

vm49.dat

Test Case

Two wires of very small radius in a quadpole device system carry a positive charge, q₁, and are located on the X-axis at positive and negative distances, d, from the origin, O. Two wires of the same radius carry a negative charge, q₂, and are located on the Y-axis at positive and negative distances, d, from the origin, O. All wires extend in the Z-direction. Determine the electric potential, V, produced out to a radius of 470 mm measured from the origin, O.

Figure 66: Quadpole Wires Problem Sketch

Material Properties

Geometric Properties

ε _o = 8.85 x 10^-12 F/m

d = 25.4 mm

q₁ = +10^-6 C/m

q₂ = -10^-6 C/m

Analysis Assumptions and Modeling Notes

Two dimensional PLANE121 quad elements are used out to the radius of 470 mm. At this radius INFIN110 elements (also quad) with radial length equal to 470 mm are used. The infinite boundary is therefore modeled to 940 mm, twice the radius of interest. Due to symmetry, only one quadrant (positive X and positive Y) is modeled with flux-normal boundary conditions at X = 0.0 and Y = 0.0. Only half of each wire in the first quadrant is included in the model by specifying one-half the charge magnitudes of q₁ and q₂.

Note: Since 4-node INFIN110 elements are used with 8-node PLANE121, the infinite element domain must be meshed before the finite element domain to force the PLANE121 element faces to automatically drop their midside nodes at the interface of the finite and infinite element domain.

The SF command with Lab = INF is used to flag the exterior surface of the INFIN110 elements as the infinite surface. The charge is applied as a point load at the center of each of two wires.

In POST1, electric potentials V every 9° from 0 to 90° at the radius 470 mm are retrieved and written by the *VWRITE command.

Results Comparison

V (Volt)	Target	Mechanical APDL	Ratio
@ Angle 0°	105.05	105.79	1.01
@ Angle 9°	99.90	100.62	1.01
@ Angle 18°	84.98	85.59	1.01
@ Angle 27°	61.74	62.18	1.01
@ Angle 36°	32.46	32.69	1.01
@ Angle 45°	0.0000	0.0000	0.0
@ Angle 54°	-32.46	-32.69	1.01
@ Angle 63°	-61.74	-62.18	1.01
@ Angle 72°	-84.98	-85.59	1.01
@ Angle 81°	-99.98	-100.62	1.01
@ Angle 90°	-105.05	-105.79	1.01