- #1

FallenLeibniz

- 86

- 1

Alright, so I have tried my hand at this problem but keep hitting a wall.

(NOTE: Every time I have tried to use ##\LaTeX## syntax in this post, it has not worked. As a result of this, and in the interest of making it easier for those who read this post to help me, I have attached a LaTex formatted pdf and referenced the equations in that pdf here. Please note however that it is my first time trying to use LaTex, so forgive me if I miss any subtle formatting points.

Actually, to those who read this post, would it be easier if I just wrote my full question as a pdf LaTex doc and then just attached it to whatever posts I do in the future?)

The Problem

A long, uniformly charged ribbon is located in the xz plane, parallel to

the z axis occupying the region -\infty<=z<=\infty and -a/2<=x<=a/2. The charge per

unit of area on the ribbon is \sigma.

a)Determine

My attempt

I decided that it would be easiest to attempt this problem using Cartesian

Coordinates. My separation vector is given by eq1 and its magnitude by eq2. The field vector I have come up with for

the problem is given by eq 3.

Now I start off by trying to solve the integrals for the ith component of

the field. I first do the integration with respect to x'. The results of this integration are given by eq 4 and eq 5.

Since the next integration involves integrating over the result of eq 5 with respect to z' and both parts of the difference take the same form, I decided to just substitute b for x-a/2 and x+a/2 and use the result of eq 6 to get my final answer.

Thus here is my dilemna. The value in the log expression goes to zero and

thus "blows up" the field in the process. I've been through my integration three

times over and still can not find anything wrong with it. I could really use

any assistance or insight that anyone can give me.

(NOTE: Every time I have tried to use ##\LaTeX## syntax in this post, it has not worked. As a result of this, and in the interest of making it easier for those who read this post to help me, I have attached a LaTex formatted pdf and referenced the equations in that pdf here. Please note however that it is my first time trying to use LaTex, so forgive me if I miss any subtle formatting points.

Actually, to those who read this post, would it be easier if I just wrote my full question as a pdf LaTex doc and then just attached it to whatever posts I do in the future?)

The Problem

A long, uniformly charged ribbon is located in the xz plane, parallel to

the z axis occupying the region -\infty<=z<=\infty and -a/2<=x<=a/2. The charge per

unit of area on the ribbon is \sigma.

a)Determine

**E**(**r-r'**) at (x,0,0) where x is greater than a/2.My attempt

I decided that it would be easiest to attempt this problem using Cartesian

Coordinates. My separation vector is given by eq1 and its magnitude by eq2. The field vector I have come up with for

the problem is given by eq 3.

Now I start off by trying to solve the integrals for the ith component of

the field. I first do the integration with respect to x'. The results of this integration are given by eq 4 and eq 5.

Since the next integration involves integrating over the result of eq 5 with respect to z' and both parts of the difference take the same form, I decided to just substitute b for x-a/2 and x+a/2 and use the result of eq 6 to get my final answer.

Thus here is my dilemna. The value in the log expression goes to zero and

thus "blows up" the field in the process. I've been through my integration three

times over and still can not find anything wrong with it. I could really use

any assistance or insight that anyone can give me.

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