Representing Electric Fields

Positive charge acting on a test charge

The magnitude of the force that a test charge experiences due to another charge is governed by Coulomb's law. In the diagram below, at each point around the positive charge, \(+Q\), we calculate the force a positive test charge, \(+q\), would experience, and represent this force (a vector) with an arrow. The force vectors for some points around \(+Q\) are shown in the diagram along with the positive test charge \(+q\) (in red) located at one of the points.

At every point around the charge \(+Q\), the positive test charge, \(+q\), will experience a force pushing it away.This is because both charges are positive and so they repel each other. We cannot draw an arrow at every point but we include enough arrows to illustrate what the field would look like. The arrows represent the force the test charge would experience at each point. Coulomb's law is an inverse-square law which means that the force gets weaker the greater the distance between the two charges. This is why the arrows get shorter further away from \(+Q\).

Negative charge acting on a test charge

For a negative charge, \(-Q\), and a positive test charge, \(+q\), the force vectors would look like:

Notice that it is almost identical to the positive charge case. The arrows are the same lengths as in the previous diagram because the absolute magnitude of the charge is the same and so is the magnitude of the test charge. Thus the magnitude of the force is the same at the same points in space. However, the arrows point in the opposite direction because the charges now have opposite signs and attract each other.

Electric fields around isolated charges - summary

Now, to make things simpler, we draw continuous lines that are tangential to the force that a test charge would experience at each point. The field lines are closer together where the field is stronger. Look at the diagram below: close to the central charges, the field lines are close together. This is where the electric field is strongest. Further away from the central charges where the electric field is weaker, the field lines are more spread out from each other.

We use the following conventions when drawing electric field lines:

• Arrows on the field lines indicate the direction of the field, i.e. the direction in which a positive test charge would move if placed in the field.

• Electric field lines point away from positive charges (like charges repel) and towards negative charges (unlike charges attract).

• Field lines are drawn closer together where the field is stronger.

• Field lines do not touch or cross each other.

• Field lines are drawn perpendicular to a charge or charged surface.

• The greater the magnitude of the charge, the stronger its electric field. We represent this by drawing more field lines around the greater charge than for charges with smaller magnitudes.

  

Some important points to remember about electric fields:

• There is an electric field at every point in space surrounding a charge.

• Field lines are merely a representation – they are notreal. When we draw them, we just pick convenient places toindicate the field in space.

• Field lines exist in three dimensions, not only in two dimension as we've drawn them.

• The number of field lines passing through a surface is proportional to the charge contained inside the surface.