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Suppose we have an electric potential that is a function of z and the distance in the transverse plane, ri = Vx2 + y². In other words, ø → ø(r1, z). Show that the gradient can be written az + Tl- 2 + y² + z², 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 Vø ar

Suppose we have an electric potential that is a function of z and the distance in the transverse plane, ri = Vx2 + y². In other words, ø → ø(r1, z). Show that the gradient can be written az + Tl- 2 + y² + z², 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 Vø ar

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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
Transcribed Image Text: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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