Electricity and Magnetism

4–34 Electricity and Magnetism

This electric field resembles that of a long straight wire.

a, b ≫ L IF both dimensions of the plate are much larger than the distance to the field

point, viz., {a, b} ≫ L, THEN the field should be not unlike that above an infinite uniformly

charged plane.

Here, the argument of the inverse-tangent function exhibits limiting behaviour which is

qualitatively and quantitatively distinct from the prior two cases:

lim

{a,b}≫L

a b

L

√

L

2

+ a

2

+ b

2

→ ∞!

There is no pathology associated with this, because

lim

x→∞

tan

−1



x



→

π

2

.

In this limit, the electric field approaches a constant value:

E

z

∼ 4 k σ

0

h

π

2

i

= 2 π k σ

0

.

This is just like the infinite