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CourseNotes.14

CourseNotes.14 - 5.2.2 Superposition Just like the electric...

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5.2.2 Superposition Just like the electric field, the electric potential obeys the law of superposition. This means that if we have multiple point charges, we can simply add up the potential due to each of them to find the overall potential. Notice that since the potential is a scaler and not a vector, we do not have to bother breaking it up into components to sum it up as we do with the electric field. Also, similar to the electric field, we can break a continuous object down into differential pieces of charge and sum up the contributions to the potential via integration. V = Z dV = 1 4 π 0 Z dq r (15) This is extraordinarily useful because we do not have to concern ourselves whit the vectorness of the electric field, but we can still calculate the field for complex objects. 5.3 Calculating the Field from the Potential The one missing piece (and one of the most important ones) is how we can connect the potential back to the electric field. Lets address that now. Recall that the fundamental theorem of calculus relates the concepts of integration and differentiation. Hence, from equation 14 we should expect
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