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Two intersecting conducting planes electric field

Two conducting planes intersect at an angle β = 270°. The planes are assumed to be held at potential V. Find the electric field distribution near the corner.

Problem Type:
Plane problem of electrostatics.

Geometry:
Two conducting planes intersect at an angle 270

Given:
Relative permittivity of vacuum ε = 1;
Voltage V = 100 V.

Solution:
Open space problem is converted to the closed region problem using the "zero potential" boundary far away from the studying object.

intersecting planes electric field

Comparison of results
Electric field strength distribution along the plane is shown in the table. The theoretical result is: E ~ r -1/3.

r, m

Electric field strength, V/m

QuickField

Theory
(2π/r 1/3)

0.1

13.46

13.54

0.2

10.69

10.74

0.5

7.89

7.92

1

6.3

6.28

1.5

5.52

5.49

2

5.03

4.99

3

4.43

4.36

electric field strength along plane

Reference
J.D.Jackson, Classical Electrodynamics, 3rd edition, Sect. 2.11.

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