Find Electric field due to line charge -- Intermediate E&M

[grandpa2390]

Homework Statement

https://www.dropbox.com/s/w8xmgdwwqalymm4/000407.png?dl=0

Homework Equations

I am not sure.

The Attempt at a Solution

I really don't understand how to go about this. I really need someone to help walk me through this where I can ask questions along the way. It is not so much that I don't understand what to do, I just don't understand how to do it. How to apply the Calculus. If you want to use a different problem or change the numbers or whatever, I am fine with that. I am not looking to have my homework done for me, I really need to get a grasp on how to apply Calculus to these problems. In fact, I would prefer it that way if you have time, energy, or resources to make up a different problem that uses the same techniques. But if not, explaining this one to me will work. Because I do not even understand what part b is asking me...

 

[BvU]

https://photos-1.dropbox.com/t/2/AACLL2mnzuLfCFvC2c03pnEpIia9xUMHjXhjva0bDi9cZg/12/61301665/png/32x32/3/1455591600/0/2/000407.png/ELnyvC8YpAYgBygH/AO9cOKMLGz90-IcoBaJxZOfFGenkwsVVaTbGHmVlVOk?size_mode=3&size=800x600

Your exercise author is doing exactly what you ask. Do you understand (2.6) ?
Do you understand that you need a relevant equation ?
Something along the lines of $\vec E = {1\over 4\pi\epsilon_0} {\vec r\over |\vec r|^3 }$ ?
And: you do know that PF doesn't like the 'I have no idea' attempt at solution (see guidelines).
I'll be happy to get you started on this, though.
I suppose hyperphysics didn't help, and more elementary steps are desired ?

PS you really a grandpa ?

 

[grandpa2390]

https://photos-1.dropbox.com/t/2/AACLL2mnzuLfCFvC2c03pnEpIia9xUMHjXhjva0bDi9cZg/12/61301665/png/32x32/3/1455591600/0/2/000407.png/ELnyvC8YpAYgBygH/AO9cOKMLGz90-IcoBaJxZOfFGenkwsVVaTbGHmVlVOk?size_mode=3&size=800x600

Your exercise author is doing exactly what you ask. Do you understand (2.6) ?
Do you understand that you need a relevant equation ?
Something along the lines of $\vec E = {1\over 4\pi\epsilon_0} {\vec r\over |\vec r|^3 }$ ?
And: you do know that PF doesn't like the 'I have no idea' attempt at solution (see guidelines).
I'll be happy to get you started on this, though.
I suppose hyperphysics didn't help, and more elementary steps are desired ?

PS you really a grandpa ?

yes I know PF doesn't like it. But unfortunately, I have nowhere else to turn. I do not know where to go to get an idea so I pled for help.
Unfortunately, the leap between the first class and this one is too large for me. That or it has been too long... Could you just point me towards a resource that could break it down for me? I'm going to check out MIT

 

[TSny]

Try for a discussion of a similar example. You will need to make modifications for your problem.

 

[grandpa2390]

Try for a discussion of a similar example. You will need to make modifications for your problem.

That was helpful. He definitely helped me to understand a bit of what I was lacking. I think I have enough now to attempt the problem. :)

 

[grandpa2390]

Try for a discussion of a similar example. You will need to make modifications for your problem.

so I attempted the problem with the understanding I gained from the video. I am not sure how correct my progress is. I am not sure, for example, if dQ=Lambda*dx'
if all that I have done is correct. I am not sure how to go on from here. I don't understand what is being asked. should I just take each integral and say it is E= <x , z> ?

here is my work. figured it would be easier to post images than try to type it... https://www.dropbox.com/sc/je4atkky02nybua/AAAOj4TG3I3O3vNpc8r2ZaXkaI guess I could always plug the integral into mathematica and check the value of Ez at x=0...

 

[TSny]

Your work looks good to me. I don't know whether you are expected to do the integrals "by hand" or if you are allowed to use tables or software. The integrals are not too hard.

Once you get expressions for E_x and E_y, I would think that would suffice for an answer.

The problem seems to want you to start from Eq (2.6) which expresses the integral for $\vec{E}$ in vector form with a unit vector $\hat{r}$. It asks for you to find an expression for this unit vector. But you should find that the components of the unit vector are what you found for cosθ and sinθ. So, you've essentially done that.

 

[grandpa2390]

Your work looks good to me. I don't know whether you are expected to do the integrals "by hand" or if you are allowed to use tables or software. The integrals are not too hard.

Once you get expressions for E_x and E_y, I would think that would suffice for an answer.

The problem seems to want you to start from Eq (2.6) which expresses the integral for $\vec{E}$ in vector form with a unit vector $\hat{r}$. It asks for you to find an expression for this unit vector. But you should find that the components of the unit vector are what you found for cosθ and sinθ. So, you've essentially done that.

:)

 

[grandpa2390]

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Your work looks good to me. I don't know whether you are expected to do the integrals "by hand" or if you are allowed to use tables or software. The integrals are not too hard.

Once you get expressions for E_x and E_y, I would think that would suffice for an answer.

The problem seems to want you to start from Eq (2.6) which expresses the integral for $\vec{E}$ in vector form with a unit vector $\hat{r}$. It asks for you to find an expression for this unit vector. But you should find that the components of the unit vector are what you found for cosθ and sinθ. So, you've essentially done that.

I didn't get zero when I integrated and plugged in x=0 and z=10...
the integral I got from mathematica $\frac{t-x}{z \sqrt{(t-x)^2+z^2}}$ and when I evaluate this from -L/2 to L/2, I don't get 0...

did I evaluate incorrectly.

edit: I just realized... E_x would be zero... whoops.

edit: I evaluated the e_x and it equaled zero when the point is directly in the middle of the line of charge.

edit: except if I take the E_z component and evaluate it at z=0, I get L/0... what does that mean? is it the wrong answer, or is the math saying that there is something going on if the point lies on the line...

 

[TSny]

if I take the E_z component and evaluate it at z=0, I get L/0... what does that mean? is it the wrong answer, or is the math saying that there is something going on if the point lies on the line...

If you consider the formula for the electric field of a point charge, you can see what happens as you approach the charge (r → 0). A similar thing happens for a line of charge except the field doesn't go to infinity as rapidly as for a point charge. Interestingly, if you have a two dimensional plane of charge the field remains finite as you approach the surface of the plane.