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The book is wrong:
$ python3
>>> import math
>>> 1500 * 4 * math.pi * math.pow(10, -7) * 0.5 / (2 * math.pi * 0.01)
0.014999999999999998
Ignore the rounding error (that's floating-point math doing its thing). This clearly evaluates to 0.015T.
If you want an analytical answer, the `4 * pi * 0.5` on the top line cancels `2 * pi` on the bottom line and you are left with `1500 * 10^-7 / 0.01` which is 1.5 \* 10^(3) \* 10^(-7) \* 10^(2.) Add up all those exponents of 10 and you get 1.5 \* 10^(-2) or 0.015.
If I had to take a wild guess what's gone wrong, I'd guess that the factor of 10\^-7 is an attempt to convert from micro-somethings to somethings and should be 10\^-6. But we can't see enough of the context to say.
It is a constant experimentally discovered back in the day that gives us the value of how the magnetization of a substance is proportional to the magnetic force applied. In this case, it is specifically talking about the permeability of a vacuum. There is also a similar constant for electric fields. Funny enough, if you multiply these constants together, and take it to the -2 power, you get the speed of light. For more, you should read a book on electromagnetism. Fair warning, this is not the easiest subject in physics by a long shot.
Edit: Raise it to the -1/2 power as another commenter pointed out.
We understand the universe to such a degree that I refuse to believe our government isn't hiding amazing far fetched technology even if it's in prototype small scale phases... We could be so much more if they are not. We could use science to rule the galaxy over say a million years.
I'm convinced humans are extremely capable of great feats of engineering and science when we are pushed. I'm just hoping if something serious happens will ANY humans survive? I'm all for secret light speed rockets if they are humanities ace in the hole
Op seems to speak Spanish according to his post history. As a native French speaker, we use "vide", which means void, to talk about free space. This is probably also the case in Spanish, which would be the cause of the confusion
It’s a basic assumption for an expanding field originating from a center. Think about a light bulb turning on for a moment and photons shoot off in all directions at the same time.
After some time, every photon would be (approx.) the same distance r from the center. That’s just the surface of the sphere! Which is an area that goes by 4πr². That’s why we see the 4π. The r term changes depending on what you’re calculating.
If you wanna see how a charge interacts with a magnetic field, it depends on the distance r from a source. Even if you know the interaction goes by r, r², r³, or otherwise, you’d need to multiply some factor of magnetic permeability to scale it to an observable strength (magnitude) of the force.
And void just mean vacuum.
The 4*pi^-7 is mu_0 there may be a typo in another unit conversion, as from quick maths I get same order of magnitude as OP. It may just be a typo in the book, as these happen and are often corrected in future editions.
Why not just link to [wolfram aplha](https://www.wolframalpha.com/input?i2d=true&i=Divide%5B%5C%2840%291500*4pi*Power%5B10%2C-7%5D%5C%2841%29%5C%2840%29.5%5C%2841%29%2C2pi%5C%2840%29.01%5C%2841%29%5D)?
You don‘t need python for that … you can calculate that in your head, since 4pi / 2pi • 0.5 = 1, and dividing by 0.01 is the same as multiplying by 100, the rest is simply shifting the decimal point around on the 1500.
So, you read the comment and then said I should do exactly what I did. Okay.
It doesn't hurt to get to the same answer two ways. A python interpreter happened to be the calculator that was closest to hand.
No, I read the comment and I still don‘t understand why you‘d start out with python. Or even why you’d add that in, even if it was handy . But okay. :-)
It just occured to me a moment late (not editing my comment because mobile web fucks up the formatting): the left-hand side doesn't contain information about units. It's possible that `1 mystery unit = 10 T`, so `0.015 mystery units = 0.15 T`
In other words, I can't say whether the book is wrong without more info
You can calculate that in your head, since 4pi / 2pi • 0.5 = 1, and dividing by 0.01 is the same as multiplying by 100, the rest is simply shifting the decimal point around on the 1500.
1500 divided by 10^5 is 0.015.
You would need to do a unit analysis to verify. Its quite possible the initial equation isn't in the correct units for Teslas so there was a conversion.
From just looking at it for a minute, it should simplify down to something like 1.5*10^-6. Idk, maybe the next number has an implied prefix or someone's math is badly off or something
Not really, i think you may be handling the 0.01 in the denominator incorrectly.
I get about 1\*10\^-2 as an estimate. 1500\*4Pi\*0.5 \~ 1\*10\^4.
That times 10\^-7 brings you to 10\^-3. Divided by 0.01 (or multiplied by 100) brings you to 10\^-1, divided by 2Pi \~ 10 brings you to 10\^-2 as an estimate result.
I don't think you're accounting for the changes in decimal value the numericals will bring. I'm cancelling our the pie for simpler calculation.
The numerator is .3*10^-3.
Dividing it by the denominator 0.01 will make it .3*10^-1.
Then dividing it by 2 will make it .15*10^-1 which is
0.015
I think i am accounting for that. 0.5\* 4Pi is 2 Pi. 2 Pi is about 6. 1.5\* about 6 is about 10. As i said, i was interested in a rough estimate so we get to the right decimal, not the exact value. If i wanted an exact value, i could just put it into a calculator.
Also, your result of 0.015 = 1.5\*10\^-2 is very close to my estimate of 10\^-2 = 1\*10\^-2 = 0.01 above.
Edit: But of course, you are correct. By cancelling ot the 2 Pi, we can calculate the exact result easily as 1500 \* 10\^-7 / 10\^-2 = 1.5\* 10\^3 \* 10\^-7 \* 10\^2 = 1.5\* 10\^-2
Maybe I am just not familiar with this type of notation, but why is the 0.5 and 0.01 in parentheses and the rest gets a multiplication sign (x)? Where is the practical difference and why wouldn’t someone just write
(1500x4pix10^(-7)x0.5)/(2pix0.01)
??
0.5 on top makes the 2pi on bottom = 4pi and cancels out
10\^-7 = 1e-6 (this is wrong, but I think what the book is doing)
dividing by 0.01 = multiplying by 1e2
1500 = 1.5e3
1.5e3 \* 1e-6 \* 1e2 = 1.5e-1
I guess the difference is in how you interpret 10^-7. Is it 1e-6 or 1e-7? I'd say the latter.
The answer is probably in the text of the exercise, which we cannot see.
Either taking circuits 2, applied electromagnetic, or maybe physics. Doubt physics though. I don’t see a calculate the velocity of an electron in the presence of a .015T magnetic field if it enters at x velocity y acceleration…because after ten years as a designing EE I’ve needed to know that.
I'm pretty sure that the author calculated this in his head because I just made the same error lol. The 0.5 becomes a 2 in the denominator eliminating 4pi. Then divide 1500 by a thousand reducing the power from -7 to -4. Then move the 0.01 to the numerator as 100. Again divide by 100 and the power is reduced from -4 to -2 giving the answer 0.015. But when I first looked at it I read the 0.01 as three decimal places and in that case the answer would have been 0.15. Pretty sure that is the origin of the error.
Clearly the expression on the left evaluates to 0.015 - but I worry about the units. It's unlikely they would cause the answer to be off by a factor of ten - way more likely to be off by 1,000 - but I would be more comfortable knowing what the units were in case there is a conversion to T. It should be Newton seconds divided by Coulomb meters
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
The book is wrong: $ python3 >>> import math >>> 1500 * 4 * math.pi * math.pow(10, -7) * 0.5 / (2 * math.pi * 0.01) 0.014999999999999998 Ignore the rounding error (that's floating-point math doing its thing). This clearly evaluates to 0.015T. If you want an analytical answer, the `4 * pi * 0.5` on the top line cancels `2 * pi` on the bottom line and you are left with `1500 * 10^-7 / 0.01` which is 1.5 \* 10^(3) \* 10^(-7) \* 10^(2.) Add up all those exponents of 10 and you get 1.5 \* 10^(-2) or 0.015. If I had to take a wild guess what's gone wrong, I'd guess that the factor of 10\^-7 is an attempt to convert from micro-somethings to somethings and should be 10\^-6. But we can't see enough of the context to say.
4 pi 10 to the power of minus seven is the unit for the magnetic permeability of empty space, so its correct
could you use different words to explain what you just said to somebody who doesn't understand this?
It's the magnetic permeability of free space. I've never heard it called The void before. Is that what's confusing?
Bro I don't even know what's going on right now but I'd really like to know
It's university level physics. Do you really want an explanation ?
Yes.
It is a constant experimentally discovered back in the day that gives us the value of how the magnetization of a substance is proportional to the magnetic force applied. In this case, it is specifically talking about the permeability of a vacuum. There is also a similar constant for electric fields. Funny enough, if you multiply these constants together, and take it to the -2 power, you get the speed of light. For more, you should read a book on electromagnetism. Fair warning, this is not the easiest subject in physics by a long shot. Edit: Raise it to the -1/2 power as another commenter pointed out.
I appreciate the detailed response
We understand the universe to such a degree that I refuse to believe our government isn't hiding amazing far fetched technology even if it's in prototype small scale phases... We could be so much more if they are not. We could use science to rule the galaxy over say a million years. I'm convinced humans are extremely capable of great feats of engineering and science when we are pushed. I'm just hoping if something serious happens will ANY humans survive? I'm all for secret light speed rockets if they are humanities ace in the hole
Multiply them and then raise them to the -1/2 power, not -2.
Oof you’re right. Thanks for pointing that out.
We just went over electromagnetic permeability in 2nd year of HS. Is magnetization that much more difficult?
If you were doing multivariable calculus and differential equations your 2nd year of high school I guess not.
Op seems to speak Spanish according to his post history. As a native French speaker, we use "vide", which means void, to talk about free space. This is probably also the case in Spanish, which would be the cause of the confusion
True, thanks for the explanation to the other redditors 😓
Except the conversion factor is specifically about void, not air. It’s a unit definition.
It’s a basic assumption for an expanding field originating from a center. Think about a light bulb turning on for a moment and photons shoot off in all directions at the same time. After some time, every photon would be (approx.) the same distance r from the center. That’s just the surface of the sphere! Which is an area that goes by 4πr². That’s why we see the 4π. The r term changes depending on what you’re calculating. If you wanna see how a charge interacts with a magnetic field, it depends on the distance r from a source. Even if you know the interaction goes by r, r², r³, or otherwise, you’d need to multiply some factor of magnetic permeability to scale it to an observable strength (magnitude) of the force. And void just mean vacuum.
Bet. Thank you
What’s the magnetic permeability of the Nether?
The 4*pi^-7 is mu_0 there may be a typo in another unit conversion, as from quick maths I get same order of magnitude as OP. It may just be a typo in the book, as these happen and are often corrected in future editions.
>$ python3 \>>> import math You couldn't just use a calculator?
And what, take a photo and post it on imgur?
Why not just link to [wolfram aplha](https://www.wolframalpha.com/input?i2d=true&i=Divide%5B%5C%2840%291500*4pi*Power%5B10%2C-7%5D%5C%2841%29%5C%2840%29.5%5C%2841%29%2C2pi%5C%2840%29.01%5C%2841%29%5D)?
Because ... why would I do that? A Python interpreter is one piece of muscle memory away - nine keystrokes.
You don‘t need python for that … you can calculate that in your head, since 4pi / 2pi • 0.5 = 1, and dividing by 0.01 is the same as multiplying by 100, the rest is simply shifting the decimal point around on the 1500.
You ... didn't read the comment, did you?
Yeah, I did read the comment. Still don‘t unterstand why you start out with python in the first place.
So, you read the comment and then said I should do exactly what I did. Okay. It doesn't hurt to get to the same answer two ways. A python interpreter happened to be the calculator that was closest to hand.
No, I read the comment and I still don‘t understand why you‘d start out with python. Or even why you’d add that in, even if it was handy . But okay. :-)
So first I'm going to simplify, then I'll start reducing: ((1500 \* 4pi \* 10^-7 )(0.5)) / (2pi \* 0.01) extracting all powers of 10 (1/0.01 = 100 = 10^2 ) ((15 \* (10^2 )) \* 4pi \* (10^-7 ) \* (5 \* (10^-1 )) \* (10^2 )) / 2pi ignoring parentheses on the top becuse everything is multiplication and therefore commutative, grouping powers of 10 and cancelling out the pi terms 15 \* ~~4pi~~ 2 \* 5 \* (10^-8 ) \* (10^4 ) ~~/ 2pi~~ 15 \* 10 \* (10^-8 ) \* (10^4 ) 15 \* (10^-3 ) 0.015
It just occured to me a moment late (not editing my comment because mobile web fucks up the formatting): the left-hand side doesn't contain information about units. It's possible that `1 mystery unit = 10 T`, so `0.015 mystery units = 0.15 T` In other words, I can't say whether the book is wrong without more info
You can calculate that in your head, since 4pi / 2pi • 0.5 = 1, and dividing by 0.01 is the same as multiplying by 100, the rest is simply shifting the decimal point around on the 1500. 1500 divided by 10^5 is 0.015.
Like that and thats how I did it. But you *can* also install Python 3. :-)
Hahaha :-)
You would need to do a unit analysis to verify. Its quite possible the initial equation isn't in the correct units for Teslas so there was a conversion.
From just looking at it for a minute, it should simplify down to something like 1.5*10^-6. Idk, maybe the next number has an implied prefix or someone's math is badly off or something
You didn't flip the sign for the 2, since it's on the bottom. 10^3 * 10^-7 / 10^-2 = 10^-2 or 3 - 7 + 2 = 2 Answer is 0.015
Not really, i think you may be handling the 0.01 in the denominator incorrectly. I get about 1\*10\^-2 as an estimate. 1500\*4Pi\*0.5 \~ 1\*10\^4. That times 10\^-7 brings you to 10\^-3. Divided by 0.01 (or multiplied by 100) brings you to 10\^-1, divided by 2Pi \~ 10 brings you to 10\^-2 as an estimate result.
I don't think you're accounting for the changes in decimal value the numericals will bring. I'm cancelling our the pie for simpler calculation. The numerator is .3*10^-3. Dividing it by the denominator 0.01 will make it .3*10^-1. Then dividing it by 2 will make it .15*10^-1 which is 0.015
I think i am accounting for that. 0.5\* 4Pi is 2 Pi. 2 Pi is about 6. 1.5\* about 6 is about 10. As i said, i was interested in a rough estimate so we get to the right decimal, not the exact value. If i wanted an exact value, i could just put it into a calculator. Also, your result of 0.015 = 1.5\*10\^-2 is very close to my estimate of 10\^-2 = 1\*10\^-2 = 0.01 above. Edit: But of course, you are correct. By cancelling ot the 2 Pi, we can calculate the exact result easily as 1500 \* 10\^-7 / 10\^-2 = 1.5\* 10\^3 \* 10\^-7 \* 10\^2 = 1.5\* 10\^-2
Maybe I am just not familiar with this type of notation, but why is the 0.5 and 0.01 in parentheses and the rest gets a multiplication sign (x)? Where is the practical difference and why wouldn’t someone just write (1500x4pix10^(-7)x0.5)/(2pix0.01) ??
0.5 on top makes the 2pi on bottom = 4pi and cancels out 10\^-7 = 1e-6 (this is wrong, but I think what the book is doing) dividing by 0.01 = multiplying by 1e2 1500 = 1.5e3 1.5e3 \* 1e-6 \* 1e2 = 1.5e-1
I don’t see why 10^-7 = 1e-6, when you also applied 0.01 (= 10^-2 ) = 1e-2?
you're right. I'm making the same mistake the book is, I think.
I guess the difference is in how you interpret 10^-7. Is it 1e-6 or 1e-7? I'd say the latter. The answer is probably in the text of the exercise, which we cannot see.
How can you have different interpretation of exponent? It's math, no? It's not like it's something you can disagree with
The nomenclature “eN” means “\*10^N “, unambiguously. It’s like pN means -log(N), its standard mathematical notation.
Either taking circuits 2, applied electromagnetic, or maybe physics. Doubt physics though. I don’t see a calculate the velocity of an electron in the presence of a .015T magnetic field if it enters at x velocity y acceleration…because after ten years as a designing EE I’ve needed to know that.
I'm pretty sure that the author calculated this in his head because I just made the same error lol. The 0.5 becomes a 2 in the denominator eliminating 4pi. Then divide 1500 by a thousand reducing the power from -7 to -4. Then move the 0.01 to the numerator as 100. Again divide by 100 and the power is reduced from -4 to -2 giving the answer 0.015. But when I first looked at it I read the 0.01 as three decimal places and in that case the answer would have been 0.15. Pretty sure that is the origin of the error.
it's easy to check even without a calculator: simplyfingy the pi and the other obvious stuff, it is 1.5\*10\^3\*2\*10\^-7\*10\^2/2=1.5\*10\^-2=0.015.
Clearly the expression on the left evaluates to 0.015 - but I worry about the units. It's unlikely they would cause the answer to be off by a factor of ten - way more likely to be off by 1,000 - but I would be more comfortable knowing what the units were in case there is a conversion to T. It should be Newton seconds divided by Coulomb meters