In the second column, why does F_1on3 (112) become negative but F_2on3 (84) stay
ID: 1873706 • Letter: I
Question
In the second column, why does F_1on3 (112) become negative but F_2on3 (84) stay positive in the vector addition portion?EXAMPLE 21.3 VECTOR ADDITION OF ELECTRIC FORCES ON A LINE Two point charges are located on the -axis of a coordinate system: 21.13 Our sketches for this problem. -1.0 nC is at x = +2.0 cm, and q,--3.0 nC is at x- +4.0 cm. What is the total electric force exerted by g1 and q2 ona charge q3 = 5.0 nC at x = 0? (a) our diagram of the situation (b) Free-body diagram for qs SOLUTION IDENTIFY and SET UP: Figure 21.13a shows the situation. To find the total force on qs, our target variable, we find the vector sum of the two electric forces on it. 0 93 -20cm 40 sum of EXECUTE: Figure 21.13b is a free-body diagram for q, which is repelled by q. (which has the same sign) and attracted to 12 (which has the opposite sign): Fi on 3 is in the -x-direction and F2 on 3 s in the +x-direction. After unit conversions, we have from Eq. (21.2) In the same way you can show that 3-84 we thus have F1 m3 = ( 1 12 N)i and F2 on,-(84 N). The net force n93 is F3 = Fi m3 + F2 on 3 = ( 112N)I + (84 N)1 = (-28 N) EVALUATE: As a check, note that the magnitude of q2 is three times that of qi, but q2 is twice as far from q3 as qi. Equation (21.2) n says that F2 on 3 must be 3/2-3/4 = 0.75 as large as Fion 3, This agrees with our calculated values: F2on,Kon,- 24 ., , ( 1.0 × 10-9 C)(5.0 × 10-9 C) (9.0 x 10° N m2/c2) = 1.12 × 10-4 N = 1121N (84 N)/( 112N) = 0.75. Because Fan 3 is the weaker force. the direction of the net force is that of Fi on 3-that is, in the nega- tive x-direction. (0.020 m) EXAMPLE 21.4 VECTOR ADDITION OF ELECTRIC FORCES IN A PLANE
Explanation / Answer
Its because of the basic rule that like charges repel and unlike charges attract each other.
q1 and q3 are positive, so the force F_1on3 is of repulsion, so q1 pushes q3, so it is to the left and thus negative.
q1 is positive and q2 is negative, so the force F_2on3 is of attraction, so q1 pulls q3, so it is to the right and thus positive.