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Suppose we have an electric potential that is a function of z and the distance in the transverse plane,
Vx2 + y?. In other words, o → ¢(rl,z). Show that the gradient can be written
V¢ =
dz
Similarly, suppose we have a potential that is purely a function of the distance, r =
from the origin. Show that the gradient can be written
Vx2 + y2 + z²,
Vø =
ar

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