Peoples Physics Book Version-2

13.4. Fields Due to Several Charges http://www.ck12.org

13.4 Fields Due to Several Charges

To find the field at a point due to an arrangement of charges — in fact, all electric fields arise due tosomearrangement
of charges — we find the vector sum of the individual fields:

E~net=∑

i

~Ei [3] Net Electric Field

Electric fields are used more frequently than gravitational ones because there are two types of charge, which makes
electric force and potential energy harder to keep track of than their gravitational counterparts. To apply this approach
to gravitational forces — that is, to find a net gravitational field — one needs to repeat the steps above, with mass in
place of charge (left for the reader).

Example 3

Question: For the diagram above, draw (qualitatively) the electric field vectors at the points shown using the test
charge method.

Answer: We will start with Test Charge 1. Test charges are always positive and have magnitude 1. Therefore we
know that the test charge will want to go toward the negative charge and away from the positive charge (like charges
repel and opposite charges attract). The strength of the electric field felt by the test charge is dependent on the inverse
square of the distance of the charges as shown by the equation

E=

kq

r^2

The farther away from the source of the field, the weaker the field becomes. Therefore Test Charge 1 will experience
a stronger field from the 1C charge. Because the distance from Test Charge 1 to the−1C is only slightly longer than
the distance from Test Charge 1 to the 1C charge, the vectors will be similar in length. Once we have determined the
relative scale of each vector, we can add them using the parallelogram method. The resultant vector is the electric
field at that point.

Finding the electric field at Test Charge 2 will involve all of the same steps. First we must determine which charge
Test Charge 2 is closer to. Like Test Charge 1, Test Charge 2 is closer to the 1C charge. However, Test Charge 2
is drastically closer whereas Test Charge 1 was only slightly closer. Therefore, the electric field that Test Charge 2