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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 Spring '08
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 Physics, Charge, Electric Potential, Electric charge, σ, 64 cm, 25.9 cm, uncalculable

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