Question

Explain the reason why there is no term containing the magnetic flux density $\mathbf{B}$ in the energy equation (5.17).

    Explain the reason why there is no term containing the magnetic flux density $\mathbf{B}$ in the energy equation (5.17).
Fundamentals of Plasma Physics
Fundamentals of Plasma Physics
J. A. Bittencourt 3rd Edition
Chapter 8, Problem 5 ↓
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Explain the reason why there is no term containing the magnetic flux density $\mathbf{B}$ in the energy equation (5.17).
Close icon
Play audio
Feedback
Powered by NumerAI
Jennifer Stoner Danielle Fairburn
Kathleen Carty verified

Juliet Schive and 50 other educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Recommended Videos

-
why-cant-the-electric-field-in-fig-1235b-have-a-z-component-after-all-the-magnetic-field-does

Why can't the electric field in Fig. 12.35b have a z component? After all, the magnetic field does.

Introduction to Electrodynamics

what-is-wrong-with-the-following-proof-that-there-are-no-magnetic-fields-by-electromagnetic-theory-n

What is wrong with the following "proof" that there are no magnetic fields? By electromagnetic theory, $\nabla \cdot \mathbf{B}=0,$ and $\mathbf{B}=\nabla \times \mathbf{A} .$ (The error is not in these equations.) Using them, we find $$\iiint \boldsymbol{\nabla} \cdot \mathbf{B} d \tau=0=\iint \mathbf{B} \cdot \mathbf{n} d \sigma$$ (by the divergence theorem) $$=\iint(\boldsymbol{\nabla} \times \mathbf{A}) \cdot \mathbf{n} d \sigma=\int \mathbf{A} \cdot d \mathbf{r} \quad \text {}$$ (by Stokes' theorem)since $\int \mathbf{A} \cdot d \mathbf{r}=0, \mathbf{A}$ is conservative, or $\mathbf{A}=\boldsymbol{\nabla} \psi \cdot$ Then $\mathbf{B}=\boldsymbol{\nabla} \times \mathbf{A}=\boldsymbol{\nabla} \times \boldsymbol{\nabla} \psi=0$ so $\mathbf{B}=0$.

Mathematical Methods in the Physical Sciences

Vector Analysis

The Curl and Stokes’ Theorem


*

Transcript

-
00:01 So in this problem, we're asked to look at this diagram that we're given, and we're asked why doesn't the electric field have any z component, right? we know that it has x and y, but no z, but we know that the magnetic field or the b field does.
00:18 So if we just consider one of the plates here, for a positive sheet, the field is pointing away from the plate, and for a negative chart, the field is going to be pointing toward it.
00:34 So let's say e1 is the electric field is a small section of the positive plate, right? at some random point let's i don't know call it p right this point p our electric field is going to be pointing away, right? and for our plate on top our negative charge plate, that's going to be pointing toward our plate at point p, right? and looking at the geometry that we have, i know that i've technically written this opposite in our drawing over here, but looking at this over here, notice that we would have our negative, our negative e field pointing this way.
01:43 And we would have our positive one pointing this way, right? and we know that usually our e fields always have ex, ey, and ez, right? but in this case, they don't, right? this is because our ex and our ex and our or z components rather, of our e1 and in this case for our negative plate, that would be e2, are pointing in the same exact direction.
02:19 And this is because of the geometry that we have set up, where our negative field is pointing directly toward our positive field, right? so what we're going to have happen is some of the forces in our z component, it's going to be e1 plus the negative of e2, right? we already discussed that e2 with negative...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever