ELS - Electric Fields

Electric Fields

Introduction

An electric field is an area around a charged particle where a force will be exerted on another charge object.

Every electric charge produces an electric field. It is the interaction of these electric fields that allows charges to exert forces on each other at a distance. An electric field is defined by the force it exerts on a small positive test charge, q, place within the field. Mathematically we get:

From the equation above we see that the units for measuring electric field strength are newtons/coulomb (N/C).

If we substitute in Coulomb's Law for F we get:

This equation shows how the strength of the field is determined by the strength of the charge creating the field, Q, and the distance from that charge. We assume that the magnitude of q<<Q so that q does not significantly affect the distribution of the charges creating the field.

The direction of the electric field is defined by the charge creating the field. As you can see, if a positive charge creates the field, the test charge, q, would be repelled radially away from the source charge. We use this to define the field for a positive charge as pointing away from the charge. The field for a negative source charge would point in towards the charge. Note: Don't let yourself get confused between the charge creating the field, Q, and the test charge that defines the field, q.

Electric Field Practice

Electric fields are vectors, so the fields at a point can be added using vector math.

When solving electric field problems in two dimensions use the same vector math techniques we covered in the Coulomb's Law practice problems.

 

Electric Field Self-Assessment

Two point charges, Q1 = -25 μC and Q2 = +50 μC are separated by a distance of 12 cm. The electric field at point P, a distance x away from Q1 on the other side from Q2 is zero. What is the distance x? 

Click here for the solution to the practice problem. Links to an external site.

 

Electric Field Lines

 

ELS_ElectricFields1.jpgTo help us visualize these invisible electric fields we draw electric field lines. The direction of the field lines is the direction of force on a positive test charge placed in the field. Positive source charges have field lines pointing away from them, while negative source charges have fields pointing in towards them. The density of field lines at a given point indicate the relative field strength at that point. The closer you are to a source charge, the greater the field line density and greater the electric field strength.

When multiple charges are present, their fields interact. We represent this in how we draw our electric field lines. Here are some points to remember when drawing field lines for multiple charges:

  1. Field lines start at positive charges and end at negative charges.
  2. When entering or leaving a charge, field lines are always perpendicular to the surface.ELS_ElectricFields2.PNG
  3. The number of field lines starting on a positive charge, or ending on a negative charge, is proportional to the magnitude of the charge.
  4. The direction of the electric field itself is always tangential to the field lines.

Here you see two important examples of electric field lines, those between two like charges and those between two opposite charges with the same magnitude charge. The field shown on the right, between a positive and negative charge, is know as an electric dipole.

 

Electric Field Visualization

Use the electric field applet linked to in the side bar to get a feel for what electric fields look like. You place an electric charge by clicking anywhere in the applet. Once you've place at least two charges you will see the electric field lines drawn (as well as lines of equipotential, which will be discussed later). You can change the sign and strength of the field by adjusting the slider in the upper right.

ELS_ElectricFields3.pngExperiment with fields due to:

  • two like charges of equal magnitude
  • two opposite charges of equal magnitude
  • two like charges of unequal magnitude
  • two opposite charges of unequal magnitude
  • as many different types of charges as you care to add (be careful, this has been known to cause madness)

Another important scenario to understand is the electric field between two parallel plates. By giving one plate a positive charge and the other a negative charge you can produce a constant electric field between the two plates.

If you stay away from the edges, you can place an electric field meter anywhere between the plates and find a constant E field that points from the positive plate to the negative plate. This scenario will be seen more throughout this unit.

 

Electric Field Conductors

Electric charges experience a force when placed in an electric field. When a conductor is placed in an electric field the free electrons will redistribute themselves over the conductor's surface. This ability of free electrons to rearrange their position in a conductor leads to some important consequences:

1. The electric field inside a conductor is always zero when the charges are not moving. If it were not, the force of the field would cause the electrons to rearrange themselves so that the force of the field did become zero. (See the Faraday Cage link in the sidebar for information about this awesome application)

2. Any net charge must be distributed evenly over the surface of a conductor. This should make sense. Like charges repel and will, therefore, arrange themselves in such a way as to reach an equilibrium with all charges near them. This is the same phenomenon that causes your hair to stand up when you're in contact with an electrostatic generator (often referred to as Van de Graaff generators.

3. The electric field will always be perpendicular to the surface of a conductor. If the field were not perpendicular, the charges would experience a force along the surface of the conductor and would rearrange themselves to remove this force, making the field perpendicular to the surface.

4. For uneven surfaces, charges will concentrate at the areas of greatest curvature.

 

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