ELECTROMAGNETISMLECTURE#05

Instructor:Muhammad Mateen Yaqoob

Electric Flux

Concept of electric field lines was described qualitatively in previous lecture

We now treat electric field lines in a more quantitative way

Consider an electric field that is uniform in both magnitude and direction

The field lines penetrate a rectangular surface of area A, whose plane is oriented perpendicular to the field

Number of lines per unit area (in other words, the line density) is proportional to the magnitude of the electric field. Therefore, the total number of lines penetrating the surface is proportional to the product EA

This product of the magnitude of the electric field E and surface area A perpendicular to the field is called the electric flux

Electric flux is proportional to the number of electric field lines penetrating some surface. SI Units of Electric Flux is newton-meters square per coulomb (N.m2/C)

Mateen Yaqoob Department of Computer Science

Example: Electric Flux Through a Sphere

What is the electric flux through a sphere that has a radius of 1.00 m and carries a charge of +1.00 µC at its center?

Solution:

The magnitude of the electric field 1.00 m from this charge is found using equation of electric field

Mateen Yaqoob Department of Computer Science

Electric Flux

If the surface under consideration is not perpendicular to the field, the flux through it must be less than

Mateen Yaqoob Department of Computer Science

Electric Flux

From this result, we see that flux through a surface of fixed area A has a maximum value EA when surface is perpendicular to field (when the normal to surface is parallel to field, that is, θ = 0°)

Flux is zero when surface is parallel to field (when normal to surface is perpendicular to field, that is, θ=90°)

We assumed a uniform electric field so far.

In more general situations, the electric field may vary over a surface.

Therefore, our definition of flux has meaning only over a small element of area.

Mateen Yaqoob Department of Computer Science

Electric Flux

The electric flux through this element is

Mateen Yaqoob Department of Computer Science

By summing the contributions of all elements, we obtain the total flux through the surface.

If we let the area of each element approach zero, then the number of elements approaches infinity and the sum is replaced by an integral. Therefore, the general definition of electric flux is

In general, value of electric flux depends both on field pattern and on surface

Example: Flux Through a Cube

The net flux is sum of fluxes through all faces of cube. First, note that the flux through four of the faces

Mateen Yaqoob Department of Computer Science

Problem

Mateen Yaqoob Department of Computer Science

Solution

Mateen Yaqoob Department of Computer Science

Problem

Mateen Yaqoob Department of Computer Science

Solution

Mateen Yaqoob Department of Computer Science