Studies of electric fields over an extremely wide range of magnitudes have established the validity of the superposition principle. In this case, the electric field at the location of Q 1 is the sum of the fields due to Q 2 and Q 3. The principle is illustrated by Figure 3, in which an electric field arising from several sources is determined by the superposition of the fields from each of the sources. According to this principle, a field arising from a number of sources is determined by adding the individual fields from each source. ![]() This calculation demonstrates an important property of the electromagnetic field known as the superposition principle. The magnitude of the force, which is obtained as the square root of the sum of the squares of the components of the force given in the above equation, equals 3.22 newtons. The resulting force on Q 1 is in the direction of the total electric field at Q 1, shown in Figure 3. In Cartesian coordinates, this force, expressed in newtons, is given by its components along the x and y axes by The total force on Q 1 is then obtained from equation () by multiplying the electric field E 1 ( total) by Q 1. The fields E 1,2 and E 1,3, as well as their sum, the total electric field at the location of Q 1, E 1 ( total), are shown in Figure 3. Thus, the total electric field at position 1 (i.e., at ) is the sum of these two fields E 1,2 + E 1,3 and is given by The electric field at the location of Q 1 due to charge Q 3 is in newtons per coulomb. The electric field at the position of Q 1 due to charge Q 2 is, just as in the example above, in newtons per coulomb. It is also clear that these two forces act along different directions. From the sign of the charges, it can be seen that Q 1 is repelled by Q 2 and attracted by Q 3. The locations of the charges, using Cartesian coordinates are, respectively,, , and metre, as shown in Figure 3. There are now three charges, Q 1 = +10 −6 C, Q 2 = +10 −6 C, and Q 3 = −10 −6 C. To illustrate this, a third charge is added to the example above. The force on Q 1 can be obtained with the same amount of effort by first calculating the electric field at the position of Q 1 due to Q 2, Q 3,…, etc. This sum requires that special attention be given to the direction of the individual forces since forces are vectors. ![]() When there are several charges present, the force on a given charge Q 1 may be simply calculated as the sum of the individual forces due to the other charges Q 2, Q 3,…, etc., until all the charges are included. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.This Time in History In these videos, find out what happened this month (or any month!) in history. ![]() ![]() #WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.
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