Notes: Electric Fields (20.4-20.5, 20.7)The Field Model

Electric Field

How does one charge “know” that another charge is near and therefore feel a force from that charge? How is the force transmitted through empty space from one charge to another?

We have assumed that one charge exerts a force on another. However, in the field model, it is the alteration of space around one charge that is the agent that exerts the force on the second charge.

The Force Model: One charge exerts a force directly on another force.

The Field Model: One charge modifies the space around itself and the second charge responds to the altered space. The altered space is the agent that then exerts the force.

A charge (or group of charges), known as the “source charges”, alter the space around them by creating an electric field.

Free space has a constant value of the permittivity that appears in physical relationships.

The permittivity of matter has a value different from that of free space.

If another charge is placed in that electric field, it will experience a force exerted by the field.

Other field models: alteration of space around a mass: alteration of space around a magnet:

The electric field can also be referred to as the force-to-charge ratio, calculated by:

Units:

Direction is defined as:

Summary

Notes: Electric Fields (20.4-20.5, 20.7), cont.Sample Problem

Sample Problem

Sample Problem

Electrophoresis

The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg Styrofoam bead bearing 600 excess electrons when placed in the field?

A 400 μg Styrofoam bead has 600 excess electrons on its surface. What is the magnitude and direction of the electric field that will suspend the bead in midair?

A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.

Summary

Notes: Electric Fields (20.4-20.5, 20.7), cont.Electric Field Diagrams

Electric Field of a Point Charge

Sample Problem

Electric field vectors represent the electric field at a single point in space in proximity to a point charge. We always draw field vectors based on the force on a positive test (probe) charge.

1. The electric field, a vector quantity, exists at every point in space. Electric field diagrams show a sample of the vectors, but there is an electric field vector at every point whether one is shown or not.

2. The arrow indicates the direction and strength of the field at the point to which it is attached – at the point where the tail of the vector is placed. The length of any vector is significant only relative the lengths of other vectors.

3. Although we have to draw vectors across the page, an electric field does not “stretch” from point to another. Each vector represents the electric field at one point in space.

4. If the probe/test charge is positive, the electric force will point in the same direction as the electric field vector. If the probe/test charge is negative, the electric force will point in the opposite direction of the field vector.

There is an isolated point charge of q =+15 μC in a vacuum. Determine the electric field at point P, which is 0.20 m to the left of the point charge.

Summary

Notes: Electric Fields (20.4-20.5, 20.7), cont.Superposition

Sample Problem

Electric Dipoles

Sample Problem

Check Your Understanding

The electric field due to multiple charges is the vector sum of the electric field due to each of the charges.

The figure shows two charged objects, A and B. Each contributes as follows to the net electric field at point P: EA=4.00 N/C directed to the right, and EB=3.00 N/C directed downward. Thus, EA and EB are perpendicular. What is the net electric field at P?

A dipole consists of a positive and negative charge separated by 1.2 cm, as shown. What is the electric field strength at a point 1.2 cm to the right of the positive charge?

A positive point charge +q is fixed in position at the center of a square, as the drawing shows. A second point charge is fixed to either corner B, corner C, or corner D. The net electric field at corner A is zero. (a) At which corner is the second charge located? (b) Is the second charge positive or negative? (c) Does the second charge have a greater, a smaller, or the same magnitude as the charge at the center?

Summary

A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?