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# L19_a - ELECTRIC FIELDS DUE TO CONTINUOUS CHARGE...

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ELECTRIC FIELDS DUE TO CONTINUOUS CHARGE DISTRIBUTIONS Approach: Break charge distribution into small elements (treat each as a point charge) Write vector sum of contributions from elements Take limit as elements become infinitesimally small INTEGRAL Steps: 1 st : Draw a picture showing contribution from one charge element o i r ˆ is unit vector pointing from i q toward P o i E r is the contribution to E r due to i q 2 nd : treat i q as a point charge and find i E r o i i i i r r q k E ˆ 2 e = r

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3 rd : Do a vector sum over contributions from all i q to get an expression for E r = i i i i i r r q k E ˆ 2 e r 4 th : go to limit of small elements so sum becomes exact integral! = = r r dq k r r q k E i i i i q i ˆ ˆ lim 2 e 2 e 0 r VECTOR INTEGRAL! – don’t panic, symmetry helps
= r r dq k E ˆ 2 e r CHARGE DENSITY (Important concept) Use to convert integral over dq into integral over spatial variables (i.e.

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