Integral/ electrostatic difficulty

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pbeierle
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I have a little trouble solving Electrostatic problems (at undergraduate level) that involve volume or surface integrals when there are normal vectors involved, and one must (normally) dot this with a vector field (such as electric field) when one cannot use Gauss's law.

one such example I can recall which I cannot solve well is a hemisphere of radius R that has a charge, and one must calculate the electric field everywhere.

Can anyone give me any pointers, or direct me to some reading source so that I can improve on such problems? (I don't find Griffiths very helpful, as it is not explicit enough, nor my introductory E+M book, which only covers the simpler ones).
 
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Maybe try engineering electromagnetics by William hayt