Notes about using the Superposition Principle

G19-1. Notes about using Coulomb's Law and the Superposition Principle

We recommend having this page handy as you read section 19-3. We point out below important things to take note of in the reading.

The symbol e represents the fundamental quantum of charge, e = 1.60 x 10^-19 C. Thus, e represents a positive value. With this definition, the charges of the electron and proton would be represented as follows: q_e = -e and q_p = +e.

Page	Equation, Figure, Example Number, or Section	Notes
631	Equation 19-5	The equation gives the magnitude of the force. The charges are enclosed in absolute value signs to emphasize that the magnitudes of the charges are used in determining the magnitude of the force.
631	Figure 19-7	In the symbol F₁₂, the first subscript represents the charge on which the force acts. The second subscript represents the charge exerting the force. The force vector corresponding to F₁₂ begins on the charge on which the force acts (1) and extends away from that charge.
634	Figure 19-8	The figure shows all the forces acting on charge 1. Note that the three force vectors begin on charge 1 and extend away from it in (a). In (b), the forces are added using the head-to-tail method to determine the net force on charge 1.
634	Example 19-2	This is a net force problem, so a force diagram is drawn and the direction of +x indicated. Note that gravitational forces (mg) are not included. This is because the gravitational forces are negligible in comparison to the electrical forces in this example. The charges are given numerical subscripts to distinguish them, and the forces are subscripted as described previously. Coulomb's Law is applied in Steps 1 and 2. The absolute values of the charges are substituted into the equation. The directions of the forces are indicated with unit vectors. A negative force simply indicates that the force is opposite the direction assigned to +x. The negative sign isn't used to indicate whether an electric force is attractive or repulsive. The superposition of the forces in Step 3 is the vector sum of the two forces.
635	Active Example 19-1	You used a technique similar to this in a gravitation problem from Ch. 12. The problem was to find a location between the Earth and the Moon where the two celestial objects exerted forces of equal magnitude on a rocket.
635	Example 19-3	This is a net force problem in 2 dimensions. The only thing that makes this problem different from other 2-dimensional net force problems you've done is that the force components are calculated using Coulomb's Law.
635	Conceptual Checkpoint 19-3	Note the use of symmetry to simplify this problem. Since the charges are equal and any point on AB is equidistant from the two charges, the x-components of the forces on the negative charge will be equal and opposite and will therefore cancel. So there will be no net horizontal component of force. The y-components of the forces on the negative charge will be equal; therefore the net vertical component of the force on the negative charge will be twice that due to either of the positive charges.
637	Spherical Charge Distributions	Typically, we treat charged objects at points. This is what Coulomb's Law assumes. For the purpose of calculating electrical force, spherical objects for which the charge is uniformly distributed on the surface act as if the entire charge were concentrated at the center of sphere. This is exact, not an approximation.