# Calculate linear charge density of rod & mag. of E-field at point

• mhrob24
In summary, the conversation is about a problem involving calculating an electric field from a charged rod. The person is not concerned about the arithmetic, but more about understanding the problem and using the correct tools to solve it. They mention checking to make sure they used the correct value for a specific term in the integral. The expert advises against plugging in numbers until the final step and explains the advantages of working symbolically. They also suggest using consistent notation and avoiding numerical errors.
mhrob24
Homework Statement
Non-conducting rod of length L = 8.15 cm has charge q= -4.23 fC uniformly distributed along its length. Calculate the linear charge density and find the magnitude of the electric field at point P, a distance of 12 cm to the right of the rod.
Relevant Equations
E(linear) = Ke ∫ dq/r^2 , where dq=λdl
Here is my work done for this problem, along with a diagram of the situation. I'm not worried so much about the arithmetic because our tests are only 50 min long so the problems they give us do not require heavy integration or calculus, but you need to know what goes where in the formula. That being said, I'm more concerned with knowing whether or not I have the right understanding of how to solve this problem and if I used the right tools in the correct way in order to solve it. To make it quicker for anyone attempting to help me, I would check to make sure I plugged in the correct value for my "r^2" term in the integral (distance from source of E-field to point). That is where I believe I might have made a mistake if I made one. My thinking is that the integration here is breaking down the charged rod into extremely tiny individual chunks of charge and calculating the field felt at point (P) by each chunk, then adding it up. Therefore, as you take the electric field calculation for each chunk, the distance from the chunk of charge to point (P) will be changing. If the total length of the rod is L= .0815 m, and (P) is .12m away from the right end of the rod, then we can write an equation for the distance from point (P) to each chunk of charge on the rod as a function of x (x = the distance you are at along the rod) : r = .0815m - x + .12m

Last edited:
It's basically right, but your notation is a bit off.
It's a single integral, so it makes no sense to write da and dr in it. Drop the dr, then write da=λdr.
But then you change notation, using x for the variable distance and r for the fixed offset from the end of the rod.

And I very strongly urge you to get into the habit of working entirely symbolically. Resist plugging in numbers until the final step. It has many advantages.

mhrob24
Thanks for the quick response!

Yes, I get what you mean by having the dq and dr terms in the integral. I shouldn't have expressed it like that. Also, I do have a bad habit with writing down everything as I'm working through a problem. I assuming the main advantage of not plugging in numbers until you have to is so you don't make a numerical error as you're going along (forgetting a + or - sign, wrong number, etc..) because this does tend to happen to me on problems that require arithmetic

mhrob24 said:
Thanks for the quick response!

Yes, I get what you mean by having the dq and dr terms in the integral. I shouldn't have expressed it like that. Also, I do have a bad habit with writing down everything as I'm working through a problem. I assuming the main advantage of not plugging in numbers until you have to is so you don't make a numerical error as you're going along (forgetting a + or - sign, wrong number, etc..) because this does tend to happen to me on problems that require arithmetic
Many other advantages... easier for others to follow; allows checking sanity by dimensional consistency and consideration of boundary cases; avoids building up rounding errors; and in many cases less writing!

## 1. What is linear charge density and how is it calculated?

Linear charge density is a measure of the amount of charge per unit length along a linear object, such as a rod. It is calculated by dividing the total charge on the rod by its length.

## 2. How is the magnitude of the electric field at a point near a charged rod determined?

The magnitude of the electric field at a point near a charged rod can be determined using Coulomb's law, which states that the electric field is directly proportional to the charge on the rod and inversely proportional to the square of the distance from the rod.

## 3. What factors influence the linear charge density of a rod?

The linear charge density of a rod is influenced by the total charge on the rod and its length. The longer the rod or the greater the charge on the rod, the higher the linear charge density will be.

## 4. Can the linear charge density of a rod be negative?

Yes, the linear charge density of a rod can be negative if the charges on the rod are predominantly negative. This would indicate an excess of negative charge compared to positive charge along the length of the rod.

## 5. How does the electric field at a point change as the distance from the charged rod increases?

The electric field at a point near a charged rod decreases as the distance from the rod increases. This is because the electric field follows an inverse square law, meaning that it decreases exponentially as the distance from the source of the field increases.

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