#### Field From a Point Charge

The electric field describes the effect of a charge, or set of charges, on the region surrounding it. The electric field, E, at any point in space is a vector that represents the force, F, on a small positive test charge, q, with magnitude:

E = F/q

The electric field due to a positive charge extends radially out in all directions from the charge (because a positive test charge placed near it would feel a force pointing away from it). The electric field due to a negative charge points radially in from all directions (because a positive test charge placed near it would feel a force pointing toward it). In general, electric field lines always point from positive charges and toward negative charges.

 Five Unknown Charges - Click on the milestone icon to answer a conceptual question that will appear in the milestone window at the upper right. Click the Explanation button to see a detailed solution to the milestone question.

Consider a dipole: two charges of equal magnitude and opposite sign separated by a distance, d. What do you think the field will look like for this configuration? You can check your prediction using the simulation by recalling that if you double click on a point, the field line going through that point will be plotted. Do this for a sufficient number of points so that you have a good idea of what the field looks like.

Notice that every field line that leaves the positive charge ends on the negative charge. That is, there are just as many field lines surrounding the positive charge as the negative charge.

Now consider a configuration of two unequal charges separated by a distance, d. Construct the field lines again. Do you notice anything different?

The field lines still go from positive to negative but the number of lines surrounding the positive and negative charges differ. There are more lines leaving the positive charge than ending on the negative charge. This is because the magnitude of the positive charge is larger than the negative charge. In fact, the number of field lines starting on a positive charge, or ending on a negative charge, is proportional to the magnitude of the charge.

 Two more unknown charges - Click on the milestone icon to answer a conceptual question that will appear in the milestone window at the upper right. Remember that you can measure the magnitude of the electric field at a point by clicking on that point. Click the Explanation button to see a detailed solution to the milestone question.

In the above simulation, what is the ratio of the two charges?

Just like forces, electric fields obey the principle of superposition, which says that the net electric field due to a set of charges is the vector sum of the electric fields from each of the individual charges. That is:

Enet = E1 + E2 + E3 +...

Consider the case of a dipole again. When you look in the region immediately surrounding the positive charge, the field lines appear to be pointing radially outward just like the single positive charge you saw above. This is because the field here is dominated by the positive charge so the contribution from the negative charge is negligible. (Enet = E+ + E- with E+ much larger than E-.) Away from both charges, where both charges make significant contributions to the net field, the field lines begin to curve due to the vector nature of the sum of the two fields.

 Four charges in a square - Click on the milestone icon to answer a conceptual question that will appear in the milestone window at the upper right. Click the Explanation button to see a detailed solution to the milestone question.

In Milestone 3, if the square is 4 cm on a side, what is the magnitude of each charge?