# Electric potential, field and charge density problem check

• DaConfusion
In summary, the conversation is about finding electric potential and charge density in various scenarios. The first part involves finding the electric field using a previous answer and setting up the problem correctly. The second part involves finding the volume charge density in spherical coordinates, with different integrals needed for different regions due to varying charge distribution. The third question is seeking clarification on the use of different points for differentiation in the second part.
DaConfusion
https://www.physicsforums.com/attachment.php?attachmentid=8198&stc=1&d=1162609042
V – Electric potential

I drew the picture of basically a rod with end points a and –a on the x-axis with a point b that sits as well on the x positive axis.

Assuming that is correct, I then am asked to find the electric field using my previous answer on the same point. I did not partially derrive with respect to y or z for the j and k vector components because the original potential equation has no y or z variables which means 0.
https://www.physicsforums.com/attachment.php?attachmentid=8199&stc=1&d=1162609042

Please let me know if the problems are worked out correctly.

My next question is:

Finding the volume charge density in spherical coordinates bounded by:

https://www.physicsforums.com/attachment.php?attachmentid=8200&stc=1&d=1162609042

The formula was given by my teacher as he told us to use that in spherical charge denisty problems. He proved it through a tedious triple integral which I was not able to completely copy down.
The problem I am having is I thought I was correctly setting up the problem but when he was doing a similar problem today on magnetism i noticed his bounds resulted in having each integral with 2-3 parts. Like a to r plus r to 2a and etc. I do not understand.

DaConfusion said:
https://www.physicsforums.com/attachment.php?attachmentid=8198&stc=1&d=1162609042
V – Electric potential

I drew the picture of basically a rod with end points a and –a on the x-axis with a point b that sits as well on the x positive axis.

Assuming that is correct, I then am asked to find the electric field using my previous answer on the same point. I did not partially derrive with respect to y or z for the j and k vector components because the original potential equation has no y or z variables which means 0.
https://www.physicsforums.com/attachment.php?attachmentid=8199&stc=1&d=1162609042

Please let me know if the problems are worked out correctly.

My next question is:

Finding the volume charge density in spherical coordinates bounded by:

https://www.physicsforums.com/attachment.php?attachmentid=8200&stc=1&d=1162609042

The formula was given by my teacher as he told us to use that in spherical charge denisty problems. He proved it through a tedious triple integral which I was not able to completely copy down.
The problem I am having is I thought I was correctly setting up the problem but when he was doing a similar problem today on magnetism i noticed his bounds resulted in having each integral with 2-3 parts. Like a to r plus r to 2a and etc. I do not understand.

none of the links work for me.

all that work is mine so please help, I typed it up on microsoft equation editor 3.0 then pasted into paintbrush and uploaded it as an image.

it's been a year since I've had e&m, but the first part looks ok. I'm kind of confused on the second part, because you're saying a is a variable. i thought a was a constant? i guess it doesn't really matter, because the general formula on the axis would be a---->x

the second one requires different integrals because the charge distribution is different for different regions. so, you'd need an integral for each of those regions to accurately calclulate stuff. i.e. 0->a, a->2a -- each region has a different density. make sense?

i had a rough time in e&m (even if i did get an A), so don't take my word as law.

I see, let me try and get more clarification on the 3rd question. As for the second, a was constant but I have to differentiate with respect to x for the i component. Would I use the source point or field? I considered a to be the source which is technically x so i showed that by differentiating with respect to a.

## What is electric potential?

Electric potential is the amount of potential energy per unit charge at a specific point in an electric field. It is measured in volts (V) and represents the work needed to move a unit charge from one point to another in an electric field.

## What is an electric field?

An electric field is a region in which electrically charged particles, such as electrons and protons, are affected by the force of electricity. It is created by the presence of electric charges and is measured in volts per meter (V/m).

## How is electric potential calculated?

Electric potential can be calculated by dividing the work done in moving a charge from one point to another by the amount of charge moved. It can also be calculated using the equation V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge, and r is the distance between the charges.

## What is charge density?

Charge density is the amount of electric charge per unit volume at a given point in an electric field. It is measured in coulombs per cubic meter (C/m3) and can be either positive or negative depending on the type of charge present.

## How can electric potential and field be used to solve problems?

Electric potential and field can be used to solve problems involving the movement of charges in an electric field, such as calculating the force exerted on a charge or determining the direction of the electric field. They are also important in understanding and designing electrical circuits and devices.

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