# Coulomb's Law

flyingpig

## Homework Statement

[PLAIN]http://img547.imageshack.us/img547/7932/14207376.png [Broken]

[PLAIN]http://img684.imageshack.us/img684/719/75458442.png [Broken]

[PLAIN]http://img88.imageshack.us/img88/4883/55224430.png [Broken]

Assume $$q_{1}=q_{2}=q_{3}$$ and that all charges are positive.

## The Attempt at a Solution

*if someone could, please tell me the proper code for vectors, because I am having trouble

For the first of the problem

$$\vec{E_{1}} = \vec{E_{21}}$$

Since it sort of just "sits in space", I put q_{2} on the origin.

So $$\vec{E_{21}} = <0, k\frac{q_2}{d^2}>$$ and the magnitude should simply be $$k\frac{q_2}{d^2}$$.

For the second part

$$\vec{E_{1}} = \vec{E_{21}} + \vec{E_{31}}$$

$$\vec{E_{31}} = k\frac{q_{3}}{d^2}<-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}>$$

Since $$\vec{E_{21}} = <0, k\frac{q_2}{d^2}>$$

Then the sum would be $$\vec{E_{1}}= \frac{k}{d^2}<-q_{3}\frac{\sqrt{2}}{2}, q_{3}\frac{\sqrt{2}}{2} + q_{2}>$$

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## Answers and Replies

Homework Helper
hi flyingpig!

(it's easiest to use bold letters for vectors )

i] the field is kq/d2, but the force is kqq/d2

ii] i think you're using 45° for the angle, it's 60°

iii] don't forget the question says you can assume the qs are all the same!

flyingpig
hi flyingpig!

(it's easiest to use bold letters for vectors )

i] the field is kq/d2, but the force is kqq/d2

ii] i think you're using 45° for the angle, it's 60°

iii] don't forget the question says you can assume the qs are all the same!

Oh right...what am I doing!!!? I was reading "electrostatic" and it immediately turned into field.

But what if I want to use arrows? I actually find it more difficult to tell if it is bold.

$$\vec{F_{1}} = \vec{F_{21}}$$

$$\vec{F_{21}}= k\frac{q^2}{d^2}<0,1>$$

That's part one

For part two

$$\vec{F_{1}} = \vec{F_{21}} + \vec{F_{31}}$$

$$\vec{F_{31}}= k\frac{q^2}{d^2}<-\frac{\sqrt{3}}{2}, \frac{1}{2}>$$

$$\vec{F_{21}}= k\frac{q^2}{d^2}<0,1>$$

So the sum of $$\vec{F_{21}} + \vec{F_{31}}$$ is then

$$k\frac{q^2}{d^2}<-\frac{\sqrt{3}}{2}, \frac{3}{2}>$$

So now, my question is, should I turn this into a unit vector?

cupid.callin
Oh right...what am I doing!!!? I was reading "electrostatic" and it immediately turned into field.

Try to be polite next time.

______________________________________________________

No, why would turn this into a unit vector?
Unit vector has mag of 1
it will mean that that your force also has a unit vector of one!!!

flyingpig
Try to be polite next time.

______________________________________________________

No, why would turn this into a unit vector?
Unit vector has mag of 1
it will mean that that your force also has a unit vector of one!!!

I wasn't being rude =(! Not sure where you caught that from.

But I thought the unit vector will only take care of the direction of my force, not the force itself? Is it okay to leave my answer above like that?

Did I get it right!??

Thanks!

cupid.callin

And direction can still be founded with this result. unit vectors just provide direction without changing mag of something!!!

10(i) + 10(j) has same direction as its unit vector (1/√2)(i) + (1/√2)(j)

flyingpig

And direction can still be founded with this result. unit vectors just provide direction without changing mag of something!!!

10(i) + 10(j) has same direction as its unit vector (1/√2)(i) + (1/√2)(j)

I noticed something, this problem just want to assume that I place q2 at the origin, why?

Also, I thought the concept of unit vector is like multiplying and dividing by one, does it really matter?

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cupid.callin
I noticed something, this problem just want to assume that I place q2 at the origin, why?
Well this problem doesnot depend on the choice of origin
Also, as long as orientation of XYZ is same direction will also remain same ... but mag of force always remain same no matter where is the origin

Homework Helper
Try to be polite next time.

cupid.callin, whatever are you talking about?
… So now, my question is, should I turn this into a unit vector?

Sort of.

The question asks for "the magnitude and direction".

So you need to find the magnitude anyway …

once you've done that, what's left is the unit vector of the direction!
I noticed something, this problem just want to assume that I place q2 at the origin, why?

Also, I thought the concept of unit vector is like multiplying and dividing by one, does it really matter?

hmmm … not sure what you mean by either of those.

flyingpig
The question asks for "the magnitude and direction".

So you need to find the magnitude anyway …

once you've done that, what's left is the unit vector of the direction!

But I thought taking the unit vector according to cep will yield a magnitude of 1N

hmmm … not sure what you mean by either of those.

Sorry I wasn't sure what my question is now that I read over again.

cupid.callin
once you've done that, what's left is the unit vector of the direction!

Both unit vector and vector itself gives same direction.
If answer is written with mag <not original vector> then only you need to give unit vector, or even better just give answer in degrees!!!

If he's giving answer in original vector, why waste time in finding unit vector also???

Homework Helper
But I thought taking the unit vector according to cep will yield a magnitude of 1N

now i'm really confused

you got kq2/x2 < -√3/2, 3/2 > …

where does 1N come into that?

you need to convert < -√3/2, 3/2 > to a magnitude times a unit vector
Sorry I wasn't sure what my question is now that I read over again.

he he

cupid.callin
you got kq2/x2 < -√3/2, 3/2 > …

where does 1N come into that?

you need to convert < -√3/2, 3/2 > to a magnitude times a unit vector

you agree that unit vector of < -√3/2, 3/2 > will have mag of 1, right?

So by this you mean that net force is just kq2/x2

< -√3/2, 3/2 > has nothing to do in the mag?

flyingpig
now i'm really confused

you got kq2/x2 < -√3/2, 3/2 > …

where does 1N come into that?

you need to convert < -√3/2, 3/2 > to a magnitude times a unit vector

he he

I got it from this

No, why would turn this into a unit vector?
Unit vector has mag of 1
it will mean that that your force also has a unit vector of one!!!

But once I get it to the unit vector, wouldn't my force be one like he said? Or is that actually not surprising since the distance is is d after all?

cupid.callin
But once I get it to the unit vector, wouldn't my force be one like he said? Or is that actually not surprising since the distance is is d after all?

Which distance is d?

Homework Helper
you agree that unit vector of < -√3/2, 3/2 > will have mag of 1, right?

So by this you mean that net force is just kq2/x2

< -√3/2, 3/2 > has nothing to do in the mag?

cupid.callin, are you drunk?

But once I get it to the unit vector, wouldn't my force be one like he said? Or is that actually not surprising since the distance is is d after all?

express < -√3/2, 3/2 > as a magnitude times a unit vector, say M <a,b> where <a,b> is the unit vector

then the magnitude of the force is M times kq2/x2, and it is in the direction of <a,b>

flyingpig
Which distance is d?

We don't know! It could be anything and it shouldn't matter

flyingpig
cupid.callin, are you drunk?

express < -√3/2, 3/2 > as a magnitude times a unit vector, say M <a,b> where <a,b> is the unit vector

then the magnitude of the force is M times kq2/x2, and it is in the direction of <a,b>

Don't you mean 1/M???

$$k\frac{q^2}{\sqrt{3}{d^2}}<-\frac{\sqrt{3}}{2}, \frac{3}{2}>$$

But then I would get back at $$k\frac{q^2}{d^2}$$

Homework Helper
hi flyingpig!

(just got up :zzz: …)

no …

for example if the vector was 3 <4,0>,

that would be 12 <1,0> …

magnitude 12, in the direction of unit vector <1,0>

flyingpig
Then what am I thinking of? For 3<4,0>

M = 12

So 1/12<12,0>?

Homework Helper
1/12 of <12,0> is the unit vector <1,0> …

are you thinking of a way to make unit vectors?

flyingpig
1/12 of <12,0> is the unit vector <1,0> …

are you thinking of a way to make unit vectors?

Isn't that the goal?

Homework Helper
half the goal …

the goal (in the original question) was to find the magnitude and the direction …

ie a magnitude and a unit vector

flyingpig
half the goal …

the goal (in the original question) was to find the magnitude and the direction …

ie a magnitude and a unit vector

$$k\frac{q^2}{\sqrt{3}{d^2}}<-\frac{\sqrt{3}}{2}, \frac{3}{2}>$$ <=== Unit vector

$$k\frac{\sqrt{3}q^2}{d^2}$$ <=== magnitude.

Homework Helper
$$k\frac{q^2}{\sqrt{3}{d^2}}<-\frac{\sqrt{3}}{2}, \frac{3}{2}>$$ <=== Unit vector

$$k\frac{\sqrt{3}q^2}{d^2}$$ <=== magnitude.

<-√3/2, 3/2> is not a unit vector

flyingpig
<-√3/2, 3/2> is not a unit vector

But I had $$\sqrt{3}$$ in the denominator.

Homework Helper
i don't understand …

are you saying that <-√3/2, 3/2> is a unit vector?

flyingpig
i don't understand …

are you saying that <-√3/2, 3/2> is a unit vector?

No, but 1/√3<-√3/2,3/2> is

Homework Helper
No, but 1/√3<-√3/2,3/2> is

yeeees … why not just write it < -1/2, √3/2 > ?

(btw, you could have seen, just by looking at the original diagram, that the angle was going to be 30° )

flyingpig
yeeees … why not just write it < -1/2, √3/2 > ?

(btw, you could have seen, just by looking at the original diagram, that the angle was going to be 30° )

That's what I had here

$$k\frac{q^2}{\sqrt{3}{d^2}}<-\frac{\sqrt{3}}{2}, \frac{3}{2}>$$

But when I take the magnitude, it will be one, not √3 of the force.

Homework Helper
we seem to be completely misunderstanding each other

i'm saying that < -√3/2, 3/2 > is not a unit vector, so it shouldn't be part of the answer …

why do you keep writing it? what is it for?

flyingpig
we seem to be completely misunderstanding each other

i'm saying that < -√3/2, 3/2 > is not a unit vector, so it shouldn't be part of the answer …

why do you keep writing it? what is it for?

But 1/√3<-√3/2, 3/2> is

I had a √3 beside a d^2

Do you see?

Homework Helper
yeees …

but, as i said, why do you keep writing < -√3/2, 3/2 > as part of the final answer?

it's not a unit vector, so what is it there for?

flyingpig
yeees …

but, as i said, why do you keep writing < -√3/2, 3/2 > as part of the final answer?

it's not a unit vector, so what is it there for?

But it isn't <-√3/2, 3/2>, it is 1/√3<-√3/2,3/2>

flyingpig
Are we going in circles?