40 Week 1: Discrete Charge and the Electrostatic Field
charge is not nailed down and can moveat allin response to the test charge, it would rearrange
and therebychangethe field one is trying to measure. By letting it go to zero, one also causes any
disturbance caused by the measurement to go to zero, leaving youwith the field that is there in the
absence of all charges.
So much for a single charge, but as we noted above, there arelotsof charges in eventiny
chunks of matter. We need a way of finding the total field producedby many charges, not just one.
Furthermore, that way needs to work for charges counted “oneat a time” (when there are only a
few and they are enumerable) and it also needs to be useful in the limitof so many charges that a
coarse-grained average yields an approximately continuouscharge distributionin bulk matter.
Fortunately for all concerned, the fields of many charges simply add right up! This too is a
principle of nature (and is related to the linearity of the underlying equations that are the laws of
nature). We call it theSuperposition Principle.