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- Homework Statement
- Ok, so this out of Giffth's intro to Edynamics. Problem 7.19:

A toroidal coil has a rectangular cross section with inner radius a, outer radius a+w and height h. It has N tightly wound loops. dI/dt= k. Additionally, w, h << a. Find E above center of toroid at height z.

- Relevant Equations
- B inside toroid mu NI/ 2 /PI / s; s being from cylindrical.

B outside = 0

Ok, so I understand how to find dphi/dt that is integral of -d/dt(B "dot" da). In this case I find a Phi that is a constant in space in time which causes me confusion in next step.

Edit: dphi/dt is constant...

Grithff's then says E field same as a Mag field above center of circular current. He writes the B found from solving Biot-Savart for a ring with current I, and says that in this senecio I is equal to -1/mu dPhi/dt.

Firstly, how the heck am I supposed to know to make this substitution based on the textbook?

Secondly, how does this make sense. How can I take a statement about EMF and faradays law that will gives me E dot dl of a closed loop and use that to find the E at any point in space. Especially, when the EMF is not a function of time or space!

I understand the idea that E field in this problem is equivalent to the B field in the prior problem. However, I can't explicitly understand how they are the same and I couldn't find any mathematical justification of there equivalence.

I would appreciate any help anyone can give me. This problem has frustrated me to no end. Therefore, I apologize for any moodiness while writing the problem.

Edit: dphi/dt is constant...

Grithff's then says E field same as a Mag field above center of circular current. He writes the B found from solving Biot-Savart for a ring with current I, and says that in this senecio I is equal to -1/mu dPhi/dt.

Firstly, how the heck am I supposed to know to make this substitution based on the textbook?

Secondly, how does this make sense. How can I take a statement about EMF and faradays law that will gives me E dot dl of a closed loop and use that to find the E at any point in space. Especially, when the EMF is not a function of time or space!

I understand the idea that E field in this problem is equivalent to the B field in the prior problem. However, I can't explicitly understand how they are the same and I couldn't find any mathematical justification of there equivalence.

I would appreciate any help anyone can give me. This problem has frustrated me to no end. Therefore, I apologize for any moodiness while writing the problem.

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