Coulomb's Law: Calculating Electric Field Due to Multiple Charges

[tiny-tim]

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?

 

[tiny-tim]

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?

 

[tiny-tim]

Are we going in circles?

yes … isn't that the flyingpig's natural method of travel?

i can't force you to write a unit vector!

 

[flyingpig]

yes … isn't that the flyingpig's natural method of travel?

i can't force you to write a unit vector!

This is bugging me, if I switch it to i and j notations

Namely, my final solution giving me 1.6N(-√3/2i + 3/2j) isnot a unit vector, but if 1.6N/√3(-√3/2i + 3/2j) then is a unit vector. So how do I deal with the magnitude? Should I take √3(1.6N) or a magnitude of one from my unit vector?

 

[tiny-tim]

the way to convert 1.6(-√3/2i + 3/2j) into a magnitude and a unit vector is:

1.6 √3 (-1/2i + √3/2j) ​

 

[flyingpig]

the way to convert 1.6(-√3/2i + 3/2j) into a magnitude and a unit vector is:

1.6 √3 (-1/2i + √3/2j) ​

You multiply and divided the vector by its magnitude, is that what you did? If so, then what was I doing? I can see you destributed the 1/√3 into the unit vector, but you left the top √3 beside 1.6N

 

[flyingpig]

Let me add another question to clarify the question I just asked.

Isn't 1/√3(-√3/2i + 3/2j) a unit vector? At least in my Linear Algebra Book

 

[tiny-tim]

You multiply and divided the vector by its magnitude, is that what you did? If so, then what was I doing? I can see you destributed the 1/√3 into the unit vector, but you left the top √3 beside 1.6N

i only left the √3 separate because i didn't want to bother to calculate 1.6 √3 !

Let me add another question to clarify the question I just asked.

Isn't 1/√3(-√3/2i + 3/2j) a unit vector? At least in my Linear Algebra Book

yes of course …

but it's a very strange way of writing it, when (-1/2i + √3/2j) is so much simpler, and you'll certainly lose a mark for it in the exam

 

[flyingpig]

i only left the √3 separate because i didn't want to bother to calculate 1.6 √3 !


yes of course …

but it's a very strange way of writing it, when (-1/2i + √3/2j) is so much simpler, and you'll certainly lose a mark for it in the exam

Why is that (-1/2i + √3/2j) simpler? If we are just talking about numbers here where 1.6 is a scalar (talking only about the numbers for now) then, 1.6/√3 <-√3/2, 3/2> is a unit vector, but that is not the same as 1.6√3<-1/2, √3/2>.

(sorry for switching notations all of a sudden, I have no idea what i was thinking)

In 1.6/√3 <-√3/2, 3/2>, I needed (wel, you needed) to multiply √3 again to get 1.6√3<-1/2, √3/2>

But noting that 1.6√3 is a scalar that will EXTEND the unit vector<-1/2, √3/2>, so how is that different?

 

[tiny-tim]

hi flyingpig!

Why is that (-1/2i + √3/2j) simpler?

because it's a unit vector!

If we are just talking about numbers here where 1.6 is a scalar (talking only about the numbers for now) then, 1.6/√3 <-√3/2, 3/2> is a unit vector

no it isn't!

 

[flyingpig]

hi flyingpig!


because it's a unit vector!


no it isn't!

I think I got confused with the outside scalar being inside the vector itself. In that case, why don't I just distribute the 1.6N?

 

[flyingpig]

My book says "Leave your answers in F_xi + F_yj

 

[tiny-tim]

My book says "Leave your answers in F_xi + F_yj

No, it doesn't! …

in post #1, you provided a photo of the book, it clearly says "What is the magnitude and direction … Leave your answer in algebraic form" …

you need to state the magnitude and direction !

 

[flyingpig]

Never mind, if i need to use Fxi and Fyj I will just convert it to a unit vector, that's all I really need to do.