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Old May 19th 2016, 06:36 AM   #1
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Electromagnetism

I am doing a course in electromagnetism and came across some parts in a couple of questions, which I'm not understanding where they came from, so I'm hoping someone can explain how they came about. All of these difficulties are math related.

The first of these includes figuring out where the 2r^3 came from (near the bottom of the page (on Q1 attachment). How did they use r^+r^-1(r^- + r^+) to get 2r^3?

The second of these includes figuring out where by inspection did d = a - z and c = b - a (see attachments Q2b and Q2a) come from. How does theta = 0 become d = a - z? I tried using the cosine rule and plugging in 0 for theta there but that doesn't appear to work either.

These are the only two parts that are confusing me mathematically.
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Electromagnetism-q1.png   Electromagnetism-q2a.png   Electromagnetism-q2b.png  
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Old May 24th 2016, 06:11 AM   #2
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For your first question, Note that they use the squiggly equal sign? That means "approximately equal to." If the distance 'a' is small relative to 'r', then 'r+' and 'r-' are approximately equal, and hence you can replace them with 'r'.

For the second question, starting with the equations (b) and (c) near the bottom of Q2a:

d^2 =a^2 - z^2 - 2az cos(theta)

if theta = 0, then this becomes:

d^2 = a^2 - 2az - z^2 = (a-z)^2

so d = a-z.

You can use the same reasoning on the other equation to get c = a-b.

Last edited by ChipB; May 24th 2016 at 06:22 AM.
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Old May 24th 2016, 06:17 AM   #3
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I can't believe I didn't spot that. Thanks Chip
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Old May 26th 2016, 09:00 AM   #4
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Another electromagnetism math issue

Attached is a solution to one of the questions in my problem sheets but I'm confused about how they got the final answer.

I've labelled on the attachment where it is and hoping you might be able to explain how they went from the second last part to the last part.
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Old May 26th 2016, 09:22 AM   #5
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They are calculating the cross product of two vectors: dy j and y dz i + adx j. If you evaluate the cross product you get -y dy dz k. So I think they're missing a minus sign.
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Old May 26th 2016, 09:51 AM   #6
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Nice one again Chip, I just calculated it out and the answer comes out exactly the way it. No minus sign missing

Thanks Chip
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Old May 28th 2016, 09:56 AM   #7
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Electromagnetism vectors

Hi Chip,

I am having a couple of more issue with understanding the mathematics to these attached parts.

The first involves figuring out the form after the matrix is solved (Q7 (e))

The other is Q2 which I'm really struggling with to be honest. I was hoping maybe you could explain the reasoning behind this solution.

Much appreciated as always.
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Electromagnetism-q7.png   Electromagnetism-q2.png   Electromagnetism-q2-sol-.png  
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File Type: pdf Part(e).pdf (115.8 KB, 1 views)
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Old May 30th 2016, 10:37 AM   #8
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Electromagnetism vectors cont...

Apologies Chip for all the questions.

I managed to figured out all of the above questions apart from one part of problem 3-2. I am posting the image again to show you exactly where I'm stuck at (see the circle), and as they do this again for another question I'd love to know where it comes from.

Basically, how did they go from 1/c k(hat) x E = E0/c ex - ey?

My electromag exam is Wednesday morning and would love to know how to solve this.
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Electromagnetism-problem-3-2.png  
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