23.5 - Interactive problem: fields and forces
On the right are two simulations that allow you to explore electric field diagrams,
and the relationship between electric fields and the electrostatic force.
In the first simulation, you explore the relationship between force and a field that is
created by two unequal charges: a charge of +90.0 nC and a charge of í45.0 nC. In
this simulation your task is to drag a positive test charge (+1.00 nC) into the field
and observe the direction and magnitude of the force that the field exerts on it.
After experimenting with this simulation, consider the answers to three questions.
First, is the force on the test charge greater where the field lines are closer together,
or where they are farther apart? Second, what is the relationship between the
direction of the force and the field lines? Hint: The word “tangent” must appear in
your answer. Third, what...is the air-speed velocity of an unladen swallow? (Just
kidding...But Monty Python fans know the consequences of a wrong answer.)
The uniform field in the second simulation is not caused by a single charge, or even
by a small number of charges. The strength and direction of such a field are the
same at all points. The field in this simulation points to the right, and its strength
everywhere is 100 N/C.
In the simulation, you are given three small charges, having values íq,+q, and
+2q. The negative charge is not, strictly speaking, a test charge, since test charges
have to be positive. However, all three are so small that they do not interact with
each other when they are placed in the uniform field.
Drag the three charges into the field, and observe the direction and magnitude of
the force it causes on each one. How does the direction of the force exerted by the
field differ for a positive and a negative charge? Does it exert a greater force on the
+2q charge or on the +q charge? If so, by what factor is the force greater?
If you have trouble with the questions posed by either of these simulations, review
the introduction to electric fields and electric field diagrams in previous sections.
23.6 - Electric fields caused by multiple charges
The individual fields from multiple charges can be combined to determine the overall
field they create. The net electric field at any point is the vector sum of the individual
fields due to each of the source charges. This additive property of electric fields is an
example of the principle of superposition.
To calculate the overall field at a point, you start by calculating the field vector
generated by each charge at that point. You then add the vectors together. The result is
the net electric field at that point due to all the charges. In the illustration of Concept 1
you see a diagram of the combined field generated by two equal, positive charges. We
also show the combined electric field vectors at several points in the field. In the upper
right corner of the diagram, you can see that such a vector is tangent to a curving field
line.
This method of combining fields is illustrated in detail in Concept 2 for one of the
combined field vectors. The individual field vectors caused by the two identical positive
charges at a location in space are depicted. We also draw the net field as the vector
sum of the two individual fields. At the location shown, the x components of the
contributing fields cancel out since they point in opposite directions and are of equal
magnitudes. The y components of these two fields point in the same direction. The
result is a combined field that points in the y direction, away from the two positive
charges.
At each location in a field
Enet is sum of fields of each charge
Electric field of multiple charges
Calculate field vector due to each
charge, then sum vectors to determine
net field