Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Potential of the vector field
Reply to thread
Message
[QUOTE="drynada, post: 5819478"] [h2]Homework Statement [/h2] I have a curve $$\Psi(t) = \hat h_\alpha$$ where the coordinates are $$\alpha=0, \beta=t$$ and $$\gamma=t$$ in the system. Additionaly $$x=\sqrt2 ^\alpha \cdot(sin\beta-cos\beta)\cdot \frac{1}{cosh\gamma}$$ $$y=\sqrt2 ^\alpha \cdot(cos\beta+sin\beta)\cdot \frac{1}{cosh\gamma}$$$$z=\sqrt2 ^{\alpha+1} \cdot tanh\gamma$$ [h2]Homework Equations[/h2] $$x^2 + y^2 +z^2 =r^2$$ [h2]The Attempt at a Solution[/h2] My job was to derived all normalized frame vectors of this system I did it. Later calculate the arc length $$s$$ and verify that the curve is lying on the sphere. My problem is: 1) How can I define the limits for the integral to calculate the arc length? Is the condition for the curve which is lying on the sphere correct? $$x^2 + y^2 +z^2 =r^2$$ 2) Last issue. I need to assume the vector field $$ G(\alpha,\beta,\gamma)={cosh\gamma\over \sqrt{2}^{\alpha+1}cos\beta} \hat h_\beta+{sinh\gamma\over \sqrt{2}^{\alpha+1}cos\beta} \hat h_\gamma $$ to be a conservative and determine the corresponding potential $$\phi$$. How can I determine this potential. Usually I always had 3 factors $$f_x, f_y, f_z$$ here $$f_\alpha, f_\beta, f_\gamma$$ where I was calculating integral of $$f_x$$. Later I was calculating derivatives for $$y$$ and $$z$$ from result of integral of $$f_x$$. I don't know how should I manage it with only two factors. In the beginning I just assumed that $$\int h_\alpha = 0 + C_1(\beta,\gamma)$$ but in the end I'm not getting correct result which should be $$\Phi=ln|cosh(\gamma) \cdot tan(\frac{\Pi}{4}+ \frac{\beta}{2})|+const.$$ What should I do? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Potential of the vector field
Back
Top