How Does Electromagnetic Theory Explain Forces in a Moving Rod?

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SUMMARY

This discussion focuses on the application of electromagnetic theory, specifically the law of Biot-Savart and its implications for forces in a moving rod within a magnetic field. The equations presented include B = ((μ₀)(NiA))/((2)(π)(r)) for magnetic field calculation and emf = B*W*v for induced electromotive force. The user seeks clarification on five equations related to electromagnetic fields and their physical meanings, particularly regarding the gradient operator and its application in vector calculus. The conversation highlights the complexities of understanding these concepts in the context of electromagnetism.

PREREQUISITES
  • Understanding of electromagnetic theory, particularly the law of Biot-Savart.
  • Familiarity with vector calculus, including gradient and partial derivatives.
  • Knowledge of electromotive force (emf) and its relation to magnetic fields.
  • Basic principles of circuit theory and magnetic flux.
NEXT STEPS
  • Study the law of Biot-Savart and its applications in electromagnetic fields.
  • Learn about vector calculus, focusing on the gradient operator and its physical interpretations.
  • Explore the concept of electromotive force (emf) in detail, including its derivation and applications.
  • Investigate the relationship between magnetic fields and induced currents in moving conductors.
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Students of physics, particularly those studying electromagnetism, educators seeking to clarify complex concepts, and anyone involved in electrical engineering or related fields looking to deepen their understanding of electromagnetic forces.

Fenter
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This question is a little bit more difficult. I'm not too sure if I'm in the right place to be posting this type of question- but here it is:

Type: Theory Question regarding electromagnetism

My professor is an extremely difficult person to understand. His notes are all over the place and his equations are not labeled or explained in the slightest.

At the end of his lecture, he gave five equations- None of which are labeled.

I will give you a background of what he was lecturing about with equations along the way to help you understand what was being learned (for those who have taken such a course), then I'm going to give you the five equations at the end for deciphering. Please help me! I would deeply appreciate it.

He lectured about the law of biot and Savart (spelled correctly?) by saying that all current loops induce a magnetic field such that B = ((muo)(NiA))/((2)(pi)(r)). He then proceeded to say that the derivative of the flux of a magnetic field with respect to time is the negative of electromagnetic force. He then applied this to crossbars in a circuit- which when moved at an angle to a magnetic field- would induce a current such that the force resisting it was Fb = iL x B. Since emf = d(flux)/dt = d(B*A)/dt (as given by Ampere's Law) if a rod of Length W moves along a u shaped circuit through a distance L, then d(B*A)/dt --> B*W*(dL/dt). (dl/dt) = velocity = v. Thus emf = B*W*v. This professor went on about how if current went through the rod, the rod would move through the magnetic field and gave equations to show the force that would do this. He then proceeded to show how if the rod were stopped by an external force, the rod would heat up (P = i^2R).

There is nothing more to this lecture other than the five seemingly meaningless equations at the end of the lecture.

Here are the five equations (I will use PR for the partial derivative sign)

1. (Gradient) x E = -PR(B)/PR(t)
2. E = -(Gradient)v - PR(A)/PR(t) For PR(A), A = Area of current loop
3. B = (Gradient) x A
4. (Gradient) dot B = 0
5. (Gradient) dot E = Resistivity/(Permitivity of free space)

I also appologise for the lack of vector notation. It should be pretty obvious which is a vector and which is not.

I hope you can help me with these. I appologise for not not making these equations more beautiful. I'm not sure how many other posters were able to make those images of various equations. In time, I'll figure it out. I hope it's not something as simple as reading the FAQ. In any event- this algebra should not be too difficult to read. The idea behind the lecture is there- anybody who understands the fundamentals of what was written will most definitely know what those five equations mean thus majority of the math is not necessary.

Best Regards,

- Fenter
 
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Still Stuck

I'm beginning to wonder if he was just hinting at future lectures. One of these equations has been addressed in a future lecture. HOWEVER, It's not totally addressed and the problem as to the physical meaning of the equation still puzzles me. it's E = -(Gradient)v. What in the world does the partial derivative of each component in a vector with respect to something mean? Isn't that essentially the derivative?

Furthermore, what IS gradient? I know it's an operator that takes the partial derivative of each component in a vector with respect to SOMETHING- but what? Anything? Does it need to be specified? Can anybody help me?
 

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