Vectors and Interpretation in Physics Calculations

[FeDeX_LaTeX]

Hello;

I have never really come across vectors before in physics, so could someone help me out? For example, what would be an example question and a calculation involving this;

$$\phi_m = \int \vec{B} \cdot d \vec{A}$$

Correct me if I'm wrong but is this saying that the magnetic flux is equal to the integral of the magnetic field multiplied by the area?

How do you indicate what direction you're using in your calculations? Is it simply if it is a positive or negative value, meaning one direction or the opposite direction?

Also, what are magnetic flux, magnetic field and area measured in? What exactly is "area" referring to?

Thanks.

 

[tensorbundle]

I have never really come across vectors before in physics, so could someone help me out?

Your statement is surprising. Have you not studied dynamics where you can find velocity, acceleration, force and so on as vectors?

Correct me if I'm wrong but is this saying that the magnetic flux is equal to the integral of the magnetic field multiplied by the area?

It's not an arithmetic multiplication. It's a vector multiplication. In this case we call it dot product. And the integration is a closed surface integral not a line integration. Are you familiar with double integrals? Also the scalar notion of area here is vectorized as area vector.
So you have to read as the magnetic flux is equal to the surface integral of dot product of the magnetic field and the area vector.

How do you indicate what direction you're using in your calculations? Is it simply if it is a positive or negative value, meaning one direction or the opposite direction?

No, it's not so simple like positive or negative value indicating directions. The direction is taken from the problem that you are going to solve. So no specific direction for all problems.

what are magnetic flux, magnetic field and area measured in? ?

magnetic flux is measured in weber, magnetic field in tesla and area in meter squared.

What exactly is "area" referring to

Yeah, the vector notion of area appears to be tantalizing to those at first who were exposed to vectors less. Let me make it easy for you. Area gives us a two dimensional space. Just imagine a rectangular plane. Like your physics textbook. Anyway your book may be thick. But forget its thickness for the time being. Now your book has two sides -front cover and back cover. Both the areas of front and back cover is same. So, if I tell you only the amount of area, you can't say about which side of the book I'm referring to. This problem can be solved if I introduce a vector perpendicular to the both covers of your book. Just put a pen perpendicularly on any side of your book. Then that pen is the area vector for that side of the book. It is directed upward and perpendicular to the surface of an area i.e. book cover. Now, each side of your book will have two different area vectors. They are equal in magnitude but opposite in direction. So, with the help of an area vector we can indicate which side of a plane we are dealing with.
Hope this helps.

 

[ZapperZ]

Hello;

I have never really come across vectors before in physics, so could someone help me out?

I concur with tensorbundle. You've never solved a projectile motion or inclined plane problems? That would be very odd.

Zz.

 

[FeDeX_LaTeX]

Hello;

Your statement is surprising. Have you not studied dynamics where you can find velocity, acceleration, force and so on as vectors?

Yes, but not as vectors, strangely.

It's not an arithmetic multiplication. It's a vector multiplication. In this case we call it dot product.

I've heard of those. Can you explain to me how they are calculated? i.e. finding the dot product of two vectors. I remember watching a video that explained it okay-ish, but now I've forgotten.

And the integration is a closed surface integral not a line integration. Are you familiar with double integrals?

I know how to calculate them -- but never graphically seen what they look like. What is a closed surface integral?

Also the scalar notion of area here is vectorized as area vector.

Is that what the "dA" means? Thanks. Also, how do we denote the direction of a vector?

So you have to read as the magnetic flux is equal to the surface integral of dot product of the magnetic field and the area vector.

Okay, I get it. Thanks.

No, it's not so simple like positive or negative value indicating directions. The direction is taken from the problem that you are going to solve. So no specific direction for all problems.

So how is direction denoted?

magnetic flux is measured in weber, magnetic field in tesla and area in meter squared.

Gotcha. Cheers.

Yeah, the vector notion of area appears to be tantalizing to those at first who were exposed to vectors less. Let me make it easy for you. Area gives us a two dimensional space. Just imagine a rectangular plane. Like your physics textbook. Anyway your book may be thick. But forget its thickness for the time being. Now your book has two sides -front cover and back cover. Both the areas of front and back cover is same. So, if I tell you only the amount of area, you can't say about which side of the book I'm referring to. This problem can be solved if I introduce a vector perpendicular to the both covers of your book. Just put a pen perpendicularly on any side of your book. Then that pen is the area vector for that side of the book. It is directed upward and perpendicular to the surface of an area i.e. book cover. Now, each side of your book will have two different area vectors. They are equal in magnitude but opposite in direction. So, with the help of an area vector we can indicate which side of a plane we are dealing with.
Hope this helps.

This helps very much indeed. Thank you!

 

[bp_psy]

Hello;

I've heard of those. Can you explain to me how they are calculated? i.e. finding the dot product of two vectors. I remember watching a video that explained it okay-ish, but now I've forgotten.

http://tutorial.math.lamar.edu/Classes/LinAlg/Vectors.aspx

You should take a course in Linear Algebra.

 

[tensorbundle]

Your statement is surprising. Have you not studied dynamics where you can find velocity, acceleration, force and so on as vectors?

Yes, but not as vectors, strangely.

It's not an arithmetic multiplication. It's a vector multiplication. In this case we call it dot product.

I've heard of those. Can you explain to me how they are calculated? i.e. finding the dot product of two vectors. I remember watching a video that explained it okay-ish, but now I've forgotten.

And the integration is a closed surface integral not a line integration. Are you familiar with double integrals?

I know how to calculate them -- but never graphically seen what they look like. What is a closed surface integral?

Also the scalar notion of area here is vectorized as area vector.

Is that what the "dA" means? Thanks. Also, how do we denote the direction of a vector?

Hi FeDeX_LaTeX,
After reading your response I was obliged to check your profile to get some idea about your mathematical education. I came to know that you don't like math but like physics very much and you are doing GCSE.
Well, from some of your threads I saw you are talking about Riemann zeta function, hyperbolic geometry but you do not know about surface integral. You reminded me the young mathematician of versatile genius Ramanujan who didn't have idea about complex numbers but formulated sophisticated theorems of number theory which were far ahead of his own time mathematics.
Some of your posts were related quarks,w/Z bosons, dark matter but you do not know how to calculate dot product of two vectors. That's just unimaginable.
Probably your dislike toward mathematics has caused this situation. In fact you may know many things about physics but your mathematics is really poor.
If you really like physics, love mathematics. Every theoretical physicists have to become a pure mathematician in some way of their researches. That's inevitable. Read the biographies of your famous physicists. You will know how much they used to love math.
And regarding vector dot product, you can find the topic vector algebra in any elementary math or physics book. Read math books with positive mindsets. Don't hate math.
I also used to hate math till my 11th grade. Specially when I had to solve trigonometric identities, my hatred used to increase. In the same year I was learning analytic geometry. I liked the way of representing geometric entities in term of algebraic equations. This changed my mindsets. Since then I became staunch lover of math. Now when I pick up the pen to do math and start to write the symbols, I feel divine happiness. I can't express how much I love math. Perhaps, former hatred has deepened the love.

 

[FeDeX_LaTeX]

Hello;

Thank you for the reply and for your story. My hatred for mathematics I think may have stemmed from the boredom that is the GCSE course... I absolutely adored mathematics for what it was prior to my fifteenth birthday, and I even began to do research of my own, looking at the distribution of prime numbers for days. But when my GCSE year started, everything seemed so wrapped up in tedium and dullness that my mathematical obsessions seemed to shrivel and my love for physics came about out of nowhere -- I dreaded physics before, yet now I adore it more for what it is. It's as if the two switched. I aim to seek the balance to love the two in future... such is my ambition. I did devote a lot of my time to educating and honing my ability in mathematics, but the very terrible consequence of doing this was that I tried to learn things that I perhaps shouldn't have; I learned things about calculus and several parts of the A-Level modules four years before I would actually be taking them, and only now have I realized that it was utterly pointless, since my desire to take the modules earlier was not actually possible due to my school's limitations. I recall reading an entire copy of Heinemann's Decision Mathematics (D1-D2) just before I came to hate mathematics.

As you might imagine, as a very young, inquisitive and rather... stupid individual, I do look up to you, and anyone who posts on this forum with such a high degree of intelligence that I one day hope to possesses myself.

Since we're leaning off on a tangent here, thank you for the advice regarding the dot product -- I will find out about it, definitely.

Thanks.

 

[FeDeX_LaTeX]

I have one question, is the dot product the same as the cross product? I am reading about it now.

 

[jtbell]

I have never really come across vectors before in physics, so could someone help me out?

You can try Hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/Hbase/vect.html#veccon

But it sounds like what you really need is a calculus-based introductory university physics textbook like Halliday/Resnick/Walker or Tipler/Mosca. There are several other common textbooks at that level, at least in the USA. I don't know what's used in the UK where you are, if I remember correctly.

Also, what are magnetic flux, magnetic field and area measured in? What exactly is "area" referring to?

For magnetic flux, again try Hyperphysics, or better, a textbook like the above.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html

 

[bp_psy]

I have one question, is the dot product the same as the cross product? I am reading about it now.

I see you didn't bother with the link so let me try again.

Dot Product

http://tinyurl.com/ybs8fae"

 

[FeDeX_LaTeX]

I didn't find anything about the cross product or dot product in the link you gave me in the post, which is why I'm asking... unless I missed it.

 

[bp_psy]

I didn't find anything about the cross product or dot product in the link you gave me in the post, which is why I'm asking... unless I missed it.

http://tutorial.math.lamar.edu/Classes/LinAlg/Dot_CrossProduct.aspx
It is the second part of the section on vectors.
The answer is no the dot and cross product are different things and have different applications.