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: Ex == av Əx' av dy' Ez = av 5v əz partial derivative OV/ox means that to take the derivative with respect to x while treating y and z as stant. The electric potential in a region of space is given by 183²
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: Ex == av Əx' av dy' Ez = av 5v əz partial derivative OV/ox means that to take the derivative with respect to x while treating y and z as stant. The electric potential in a region of space is given by 183²
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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
Ey
ây'
The partial derivative OV/Ox 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
Ex
=
What is the electric field in this region?
av
Əx'
2
5y
V (x, y, z) = V. ((-)² – 57)
av
əz
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