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Lecture 2 The Electric Field.

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Chapter 15.4 15.9

Outline

- The Concept of an Electric Field
- Electric Field Lines
- Electrostatic Equilibrium
- Electric Flux and Gauss’ Law

In order to describe the interaction process under these forces, a concept of a field was introduced.

Both the gravitational and electrostatic force act through space, involving no contact between the objects involved.

An electric field is said to exist in the region of space around a charged object.

When another charged object enters this electric field, the field exerts a force on the second object.

Consider a small charge q0 near a larger charge Q.

We define the electric field E at the location of the small test charge as a ratio of the electric force F acting on it and the test charge q0

F

E

q0

This is the field produced by the charge Q, not by the charge q0

The direction of E at a point is the direction of the electric force that would be exerted on a small positive test charge placed at that point.

Once the electric field is known at some point, the electric force on any charge q0 placed at that point is:

|Q| |q0|

F = ke

r2

F = q0E

|Q|

E = ke

r2

This is the electric field due to a charge Q. Units N/C.

If Q is positive, then the field is radially outward from it.

If Q is negative, then the field is radially toward it.

To visualize electric field patterns, one can draw lines pointing in the direction of the electric field vector at any point.

These lines are called electric field lines.

The electric field vector is tangent to the electric field lines at each point.

The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region.

No two field lines can cross each other.

In conductors, electrons are free to move within the material.

When no net motion occurs within a conductor, it is said to be in electrostatic equilibrium.

- Properties of an isolated conductor:
- The electric field is zero everywhere inside it.
- Any excess of charge resides entirely on its surface.
- The electric field just outside a charged conductor is perpendicular to its surface.
- On an irregularly shaped conductor, the charge accumulates at sharp points.

Let’s consider a uniform electric field in both magnitude and direction which penetrates a surface of area A, perpendicular to the field.

The number of electric field lines N per unit area A (N/A) is proportional to the field magnitude (E), EN/A N EA.

This quantity is called the electric flux, E.

If the surface is not perpendicular to the field, then E = EA cos , where the normal to the area A is at an angle with respect to the field.

If the area is represented by a closed surface, flux lines passing into the interior of the volume are negative and those passing outside are positive.

Consider a point charge q at the center of a sphere of radius r. The electric field magnitude at any point on the surface of the sphere is:

|q|

E = ke

r2

|q|

E = EA = ke 4 r2 =4 ke|q|

r2

The constant є0 = 1/ 4 ke is called the permittivity of free space.

Gauss’ Law: the electric flux through any closed surface is equal to the net charge inside it divided by the є0

E = q / є0

Electric field is a concept, allowing to understand the action of the electric force.

The directions of the electric field at a point source is the direction of the electric force exerted on a small positive charge.

- Electric flux through a surface is a product of the electric field magnitude and the surface area.

- Gauss law allows to calculate the electric flux through any closed surface