v + t = as the little sphere moves away, the force it feels and its acceleration both decrease. Nevertheless, because the acceleration of the little sphere always points in the same direction (namely, away from the big sphere), the speed of the little sphere is always increasing, although the rate of increase of speed gets smaller as the little sphere gets farther away. The Principle of Superposition for Electric Forces Coulomb's law tells us how to calculate the force that one charge exerts on another one. What if two (or more) charges affect a third one? For example, what is the electric force on g, in the following figure? '@ . @ SF R Here's the answer: If F| , is the force that q, alone exerts on g,(ignoring the presence of g,) and if F,_,, , is the force 2 that g, alone exerts on g, (ignoring the presence of ,), then the total force that g, feels is simply the vector sum Fy ,, 4 + Fy o4 The fact that we can calculate the effect of several charges by considering them individually and then just adding the resulting forces is known as the principle of superposition. (This important property will also be used when we study electric field vectors, electric potential, magnetic fields, and magnetic forces.) - The Principle of Superposition The net electric force on a charge (q) due to a collection of other charges (Q's) is equal to the sum of the individual forces that each of the Q's alone exerts on q. '@ '13 q 2 Example 9-7: In the figure above, assume that , = 2C,q, = -8 C,and y = 1 nC.Ifr = 1 mand R = 2 m, which one of the following vectors best illustrates the direction of the net electric foree on g4? AN A B. / D. / Solution: The individual forces F_, ,and F, , are shown in the figure below. Adding these vectors gives F,, ,, which points down to the right, so the answer is C, '@ 11:24 a l j ... ONall 31% Physics_and M... Q . . . r + 913 R Example 9-7: In the figure above, assume that q, = 2 C, q2 = -8 C, and q3 = 1 nC. If r = 1 m and R = 2 m, which one of the following vectors best illustrates the direction of the net electric force on q;? A. C. B. D. Solution: The individual forces F1-on-3 and F2-on-3 are shown in the figure below. Adding these vectors gives Fon 3, which points down to the right, so the answer is C. 226/490 ... .. . 2-on-3 93 + F 1-on-3 + on 3 = 1-on-3 + 2-on-3 Fi-on-3 = k 4193 = 9 x 10'- N . m (2 C)(1 x 10 ' C) C2 =18N (1 m) (repulsive; away from q,) F2-on-3 = k 192 93 = 9 x 109 N .m (8 C)(1 x10 ' C) R 2 C 2 =18N (2 m) (attractive; toward q2) If the question had asked for the magnitude of the net electric force on q3, then we'd use the Pythagorean theorem to find the length of the vector Fon 3. The vector Fon ; is the hypotenuse of the right triangle whose legs are F1-on-3 and F2. on-3, so the magnitude of Fon 3 is found like this: O