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

Results:
Electric field strength distribution along the plane is shown in the table.

r, m

Electric field strength, V/m

QuickField

Reference *
(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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r, m	Electric field strength, V/m
r, m	QuickField	Reference * (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