21.1GAUSS’S LAW 21EXERCISESSection 21.1 Electric Field Lines 18.The number of lines of force emanating from (or terminating on) the positive (or negative) charges is the same (14 in Fig. 21.31), so the middle charge is3 Cμ−and the outer ones are3 C.μ+The net charge shown is therefore3333 C.μ+−=This is reflected by the fact that 14 lines emerge from the boundary of the figure. 19. INTERPRETThis problem is about drawing field lines to represent the field strength of a charge configuration. DEVELOPWe follow the methodology illustrated in Figure 21.3. There are 16 lines emanating from charge +2q(eight for each unit of +q). Similarly, we have 8 lines ending on.q−EVALUATEThe field lines of the charge configuration are shown below. ASSESSOur sketch is similar to Fig. 21.3 (f) with twice the number of lines of force. 20.(The sketch shown follows the text’s convention of eight lines of force per charge magnitude q.) 21. INTERPRETIn this problem we are asked to identify the charges based on the pattern of the field lines. DEVELOPFrom the direction of the lines of force (away from positive and toward negative charge) one sees that Aand C are positive and Bis a negative charge. Eight lines of force terminate on B, eight originate on C, but only four originate on A, so the magnitudes of Band Care equal, while the magnitude of Ais half that value. EVALUATEBased on the reasoning above, we may write.2CBAQQQ−==+The total charge isQQA=,BCAQQQ+=soQQ.CBASSESSThe magnitude of the charge is proportional to the number of field lines emerging from or terminating at the charge. 2Q== −
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