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 HP PRIME Line Integral (BiotSavart Equation)
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HP PRIME Line Integral (BiotSavart Equation)
11152016 09:23 AM
Hello friends!
I`m trying to evaluate some integrals in this format:
Some of my especifcs values are:
dl = [a*sin(w)*dw , a*cos(w)*dw , 0] > dw is the infinitesimal increment in w
R = [a*cos(w) , a*sin(w) , z]
a=0
b=pi
I know how to operate the Cross Product of 2 generic vector, but, how can I solve this kind of integration when the infinitesimal vector is a operand of a cross product ?
Thank you for your time!
Luiz Bernardi.
Solved! Go to Solution.
11152016 02:35 PM
Hi!, @luiz_aug:
If you see, this link, you can learn and use in HP PRIME ... http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/Biosav.html
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
11152016 08:30 PM  edited 11152016 08:31 PM
Hi Maké!
I spent some time reading the link you suggested, and I got some positive results.
I choosed to work with the differential form instead of the integral form, as shown at the explanation. Here is what I did:
1 defined dB as the differential form of the BiotSavart Law:
db:= (u*j*CROSS(diff([a*cos(w),a*sin(w),0]),w),[a*cos(w),a*sin(w),z]))/(4*pi*ABS([a*cos(w),a*sin(w),z])ˆ3)
2 Now that dB is set, and is a function of w, I found the correct results by doing:
int(db,w,0,pi)
But my main doubt is right here: Why cant I simply do something like this:
I mean, I have already told the calculator that db is a diferential vector, why this operation gives me the answer pi as if I were doing the integration over a generic variable b ?
Another question that maybe helps to figure out how to do evaluate this kind of problem:
Is there some way to set the calculator to do integrals over a path, instead of doing it over a simple variable?
11162016 11:52 AM  edited 11162016 12:39 PM
Hi!, @luiz_aug:
See, the video and resolution with simplified calculus, from ... http://study.com/academy/lesson/thebiotsavartlawderivationexamples.html
Try, with this equation's, from Wolfram Alpha ... http://www.wolframalpha.com/input/?i=Biot+Savart&rawformassumption=%7B"C",+"Biot+Savart"%7D+>+%7B"P...
Have a nice day !.
@Maké (Technical Advisor Premium  HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
11162016 04:59 PM  edited 11162016 05:08 PM
Hi Jan_D
First, thank you for your time answering me!
Let me see if I undestood your strategy:
You defined dl=v*dw, then by the scalar multiplication property of the vector product you assumed that
Cross(dl,r) = Cross(v*dw,r) = dw*Cross(v,r) ?
Why did you defined dl if you dont use it at all ? Just to explicit that dl=v*dw ?
Thank you one more time!
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