P23_011 - 11. We place the origin of our coordinate system...

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Unformatted text preview: 11. We place the origin of our coordinate system at point P and orient our y axis in the direction of the q4 = −12q charge (passing through the q3 = +3q charge). The x axis is perpendicular to the y axis, and thus passes through the identical q1 = q2 = +5q charges. The individual magnitudes E1 , E2 , E3 , and E4 are figured from Eq. 23-3, where the absolute value signs for q1 , q2 , and q3 are unnecessary since those charges are positive (assuming q > 0). We note that the contribution from q1 cancels that of q2 (that is, E1 = E2 ), and the net field (if there is any) should be along the y axis, with magnitude equal to |q4 | 12q 1 q3 3q 1 −2 ˆ= −2ˆ Enet = j j 2 2 4πε0 (2d) d 4πε0 4 d d which is seen to be zero. A rough sketch of the field lines is shown below: .. ................................. ..................................... ... . ..... .. ....... ...... .. ..... ... . .............. ..... ..... ..... .... .... .... .... .... ... ... .... .... . .. ... .. ... . .. .. .. .. .. .. . .. .. .. . .. . . . . . . . . . . . . . . . . . . . ............. ............. . . .... .... . . ..... .... . . ..... . ..... . . .. .... . .... . . . ... . ... . . ... ... . . . . ... ... . ... . ... . . . ... . . ... .. . . .. . . ... .. ... . . .. . . .. . .. . .. .. ... . . .. . ... . .. .. .. . . .. . .. . ... . . . ... . .. .. .. . ... . . .. . . .... . ... . ...... .. ...... . .. . .. . . .. ...................... ...................... .. .. ... . .. ..... ... ....................... . .. ... ................................ . . .... .... . . ... . ........ ......... . . . .. ....... ... .... .. ... .... .. . . .. .... .. . .... .. . . ..... ....... . .. . ... . .. . .... ..... . ... . .... . .... . .. . .. .. . .... . . . ... ... . ................ .. .......... ................... .......... ... ........ . . .. ... ........ . .. .. . . ...... ...... . ..... .... .. .. . ... . ... ... .. . ... ...... .. ....... . ..... . . . . ... ... .... .. ..... ....... . ........ .... .. ... . .. . . ... . ... . . . . .. . .. ... . .... ..... .... . ........ ... .... ..... .... . ........ .. . . . . . . .. .. . .. .. . .. ... .... ... . . .. .... .. . ... .. .... .... . ..... ..... . .. . . ... .. .. . .... ..... . . . .. ... . . . .. ... .. .. . ... .. . . ... .... . . . . .. . . .. ... .. . ... . .. . .. . ..... . ... . . ... ..... .. . .. . ..... .. .. . ... . . ... ... .. . . . ..... . .... . . .. . . . .... .. . ..... . ... . .. ... . . . .. .. . . . . ... . .. . ...... . . .... ... . . . . . .. . ...... ...... ... . . . . . . ... . . . . . . . . ... ... .. . ... . . ... .. .. . .. . .. . .... . . .... .. .. . ... . . . . .. . . ...... .. . . .. ..... ........ . ..... . . .. ............. . . . . .. . .... .. . . ... . ................. . . .... .. ................... . . . ..... .... . .... . .. .. .. . . . .. . . . . . . . .. . . . . . . .. . . . .. . . . . . . . . . . ... . . . .... . . .. . . .. . . . . . . .. . . . . . ... . . . . ..... . . ... . . .. . . . . . . . . .. . . . . . . . .. .. . . . . . . .. .. . .. . . . . .. . . .. .. .. . . . . .. .. . .. .. .. . . . .. . .. .. .. . ... .. .. . .. .. . .. ... .. . ... . .. ... . .. .... .. .... . .. .. .. .... . .. .. ..... .. .. . ....... ...... .... . .. .. .. ... .. .. ... .. ... .... . .. .... . .. .. ... ..... . .. ... ...... ... .. ..... ....... ..... ........ ... ... ....... . ............ ... .. .................... ........ .... .... . . ... . .... ........ ..... . ......... . ...... ........... . ....... ................ . ................................ . ..................... . . . . . .. ..... .... . .. . .. .. . • • • • ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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