Meaning of Electric Field

The Electric Field

(Chapter 22.1-5)

A. Meaning of Electric Field?

Consider Coulomb’s Law describing force between charges q1 and q2 separated by distance r:

Why does q2 ‘feel’ force?

¨  Can think of it as q1 setting up a ‘force field’ that q2 has entered

¨  The field is there irrespective of the presence of q2

¨  The field exerts a force per charge on a charge q2 that enters it.

Thus , where we are assuming q1 is a point charge, and is unit vector pointing away from q1.

Electric field is a vector field, i.e., a region of space that has vectors associated with each location. The direction of the vector is the direction of force a positive test charge would experience at that location. The magnitude of the vector is the force/per charge a test charge would experience at that location.

(Discuss similarities to the gravitational field)

B. Visualizing Electric Fields

Represented visually different ways

¨  Electric field lines (see figures 22-2b to 22-5 on pages 582 and 583)

¨  Electric field vectors (see figure 22-6 on page 584)

C. Electric Fields of Simple Charge Configurations

Electric field due to a point charge, q1, is given as in the above:

If there is more than one source, we must do vector addition to get net field due to all sources, treating each source as a point source.

Example: Like Problem 12, page 598

Calculate the direction and magnitude of the electric field at point P due to the three point charges.

The E-field contributions by the +q charges cancel each other out. The magnitude of the contribution to the E-field by the +2q charge is:

The direction is given by the remaining arrow pointing to the upper right.

Visualizing Three Special Cases:

¨  Two positive charges

¨  Two negative charges

¨  One positive and one negative charge

D. Electric Field due to Electric Dipole

Special case of at distance z from electric dipole

Assumes z > d

where p is electric dipole moment

(see pages 585-587 for development)

E. Electric Fields and Conductors

Charge a conductor. How does the charge distribute itself?

¨  Sphere

¨  Spherical shell

¨  Arbitrary solid shape

What is the electric field like inside a charged conductor?

How do electric field lines ‘meet’ a conductor?