Electricity

F, which also has a magnitude of 3.6 newtons; its direction, however, is opposite to that of F. The force F can be expressed in terms of its components along the x and y axes, since the force vector lies in the xy plane. This is done with elementary trigonometry from the geometry of Figure 1, and the results are shown in Figure 2. Thus,

• in newtons. Coulomb’s law describes mathematically the properties of the electric force between charges at rest. If the charges have opposite signs, the force would be attractive; the attraction would be indicated in equation (1) by the negative coefficient of the unit vector r̂. Thus, the electric force on Q1 would have a direction opposite to the unit vector r̂ and would point from Q1 to Q2. In Cartesian coordinates, this would result in a change of the signs of both the x and y components of the force in equation (2).

• When there are several charges present, the force on a given charge Q1 may be simply calculated as the sum of the individual forces due to the other charges Q2, Q3,…, etc., until all the charges are included. This sum requires that special attention be given to the direction of the individual forces since forces are vectors. The force on Q1 can be obtained with the same amount of effort by first calculating the electric field at the position of Q1 due to Q2, Q3,…, etc. To illustrate this, a third charge is added to the example above.

• This calculation demonstrates an important property of the electromagnetic field known as the superposition principle. According to this principle, a field arising from a number of sources is determined by adding the individual fields from each source. 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. In this case, the electric field at the location of Q1 is the sum of the fields due to Q2 and Q3. Studies of electric fields over an extremely wide range of magnitudes have established the validity of the superposition principle

• Both the rod and bracket are placed inside a long, hollow metal tube with a square cross section; this enclosure is at a potential of zero (i.e., it is at “ground” potential). Figure 6 shows the geometry of the problem. Because the situation is static, there is no electric field inside the material of the conductors. If there were such a field, the charges that are free to move in a conducting material would do so until equilibrium was reached. The charges are arranged so that their individual contributions to the electric field at points inside the conducting material add up to zero. In a situation of static equilibrium, excess charges are located on the surface of conductors. Because there are no electric fields inside the conducting material, all parts of a given conductor are at the same potential; hence, a conductor is an equipotential in a static situation.