Question

An infinite slab of charge of thickness 2z0 lies in thexy-plane between z=?z0 andz=+z0. The volume charge density ?(C/m3) is a constant.

1-Use Gauss's law to find an expression for the electric field strength inside the slab (?z0?z?z0).

Express your answer in terms of the variables ?,z, z0, and constant ?0.

2-Find an expression for the electric field strength above the slab (z?z0).

Express your answer in terms of the variables ?,z, z0, and constant ?0.

3-Draw a graph of E from z=0 toz=3z0.

Answer 1

Concepts and reason

The required concepts to solve the problem are Gauss’s law, electric charge density, electric flux and electric field.

First, equate the electric flux of the Gaussian surface to the charge density around the surface to find the electric field inside the slab. Then, equate the electric flux of the Gaussian surface to the charge density around the surface to find the electric field above the slab.

Fundamentals

According to Gauss’s law, the electric flux of a surface is times the net charge enclosed by the surface is,

Here, is the net charge enclosed by the Gaussian surface and is the permittivity of free space.

The expression for electric flux is,

Here, is the electric field andis the surface area.

The volume charge density is defined as the ratio of the total charge to the total volume.

Here, is the total charge and is the total volume.

(1)

Let there be a Gaussian surface with areainside the slab. Then the flux on both sides of the Gaussian surface is,

……(I)

The charge from the equation for the volume charge density is,

Use for V in the above expression and rewrite in terms of q.

Here, is the thickness of the Gaussian surface.

Thus, the electric flux is,

Use for q in the above expression.

…… (II)

Equating (I) and (II) to find the strength of the electric field,

(2)

The charge from the equation for the volume charge density is,

Use for V in the above expression and rewrite in terms of q.

Here, is the thickness of the slab.

Thus, the electric flux is,

…… (III)

Use for q in the above expression.

Equating (I) and (III) to find the strength of the electric field,

(3)

The graph of the electric field is,

Ans: Part 1

The expression for electric field inside the slab is .

Part 2

The expression for electric field inside the slab is .

Part 3

The graph of the electric field is,