4. Having found the voltage difference from knowing the electric field, we can also do the inverse, find the electric field if we know the voltage as a function of position. Since the inverse of integration is differentiation, we have: av Ex E₂ ау The partial derivative av/ax means that to take the derivative with respect to x while treating y and z as constant. The electric potential in a region of space is given by What is the electric field in this region? ay Ox' 5y V(x, y, z) = V. (¹-2) av az
4. Having found the voltage difference from knowing the electric field, we can also do the inverse, find the electric field if we know the voltage as a function of position. Since the inverse of integration is differentiation, we have: av Ex E₂ ау The partial derivative av/ax means that to take the derivative with respect to x while treating y and z as constant. The electric potential in a region of space is given by What is the electric field in this region? ay Ox' 5y V(x, y, z) = V. (¹-2) av az
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Transcribed Image Text:4. Having found the voltage difference from knowing the electric field, we can also do the inverse, find the
electric field if we know the voltage as a function of position. Since the inverse of integration is
differentiation, we have:
av
Ex
E₂
ау
The partial derivative av/ax means that to take the derivative with respect to x while treating y and z as
constant. The electric potential in a region of space is given by
What is the electric field in this region?
ay
Ox'
5y
V(x, y, z) = V. (¹-2)
av
az
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