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# chap21 - GAUSSS LAW 21 EXERCISES Section 21.1 Electric...

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21.1 GAUSS’S LAW 21 E XERCISES Section 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 is 3 C μ and the outer ones are 3 C. μ + The net charge shown is therefore 3 3 3 3 C. μ + = This is reflected by the fact that 14 lines emerge from the boundary of the figure. 19. I NTERPRET This problem is about drawing field lines to represent the field strength of a charge configuration. D EVELOP We follow the methodology illustrated in Figure 21.3. There are 16 lines emanating from charge +2 q (eight for each unit of + q ). Similarly, we have 8 lines ending on . q E VALUATE The field lines of the charge configuration are shown below. A SSESS Our 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. I NTERPRET In this problem we are asked to identify the charges based on the pattern of the field lines. D EVELOP From the direction of the lines of force (away from positive and toward negative charge) one sees that A and C are positive and B is a negative charge. Eight lines of force terminate on B , eight originate on C , but only four originate on A , so the magnitudes of B and C are equal, while the magnitude of A is half that value. E VALUATE Based on the reasoning above, we may write . 2 C B A Q Q Q = = + The total charge is Q Q A = , B C A Q Q Q + = so Q Q . C B A SSESS The magnitude of the charge is proportional to the number of field lines emerging from or terminating at the charge. 2 Q = = −

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