# Total induced charge of an infinite cylindrical conductor

• wgdtelr
In summary, the homework statement asks for someone to calculate the total induced charge on a charged cylinder. The surface charge density is given by sigma= 2eEo cos(phi). The integral of (sigma) da is then attempted to be solved, but it is impossible due to the infinite length of the cylinder. If cylindrical coordinates are used, the limits for r, Phi, and z can be found.

## Homework Statement

calculate total induced charge on a charged cylinder. where the surface charge density is given by sigma= 2eEo cos(phi)

## Homework Equations

the total induced charge on the cylinder is

Integral of (sigma) da

can u calculate this integral fo me ... it very urgent..

## The Attempt at a Solution

Use cylindrical coordinates $da \Rightarrow rd\phi dz$.

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Can u please give me the limits under which i'Ve to integrate for r ,Phi, z.

here it is infinite long cylinder and what limits can we take in z- direction.

You can't calculate the total charge on an infinite conductor. What you have to do is integrate over a finite piece of conductor then divide the total charge by the length of your z interval. This way you get the total charge on the conductor per length.

Cyosis said:
Use cylindrical coordinates $da \Rightarrow rdrd\phi dz$.

Surely you mean $da=rd\phi dz$...right?

Cyosis said:
You can't calculate the total charge on an infinite conductor.

Sure you can, just do the angular integral first

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wgdtelr said:
Can u please give me the limits under which i'Ve to integrate for r ,Phi, z.

Well, the entire surface is at some constant radius, so there is no need to integrate over $r$ at all.

If the cylinder is infinitely long, then the limits for $z$ are $\pm \infty$

And the limits for $\phi$ are $0$ to $2\pi$...These should all be fairly obvious to you...have you not used cylindrical coordinates before?

As for the integration, do the angular integral first!

yaaaaa I've got zero.. after doing the angular part.

Surely you mean LaTeX Code: da=rd\\phi dz ...right?

Ugh not very handy of me to write down the volume element, thanks.

Sure you can, just do the angular integral firstp

Actually looking at the function that is to be integrated might help next time!

wgdtelr said:
yaaaaa I've got zero.. after doing the angular part.

And this result should be no surprise, since an induced charge density does not change the total charge on a surface, it merely redistributes the charges. If the conductor was neutral before the charge was induced, it will still be neutral afterwards.

## 1. What is the definition of total induced charge?

The total induced charge refers to the net electric charge that is accumulated on a conductor due to the presence of an external electric field. It is caused by the movement of free electrons within the conductor.

## 2. How is the total induced charge of an infinite cylindrical conductor calculated?

The total induced charge of an infinite cylindrical conductor can be calculated using the formula Q = λl, where Q is the total induced charge, λ is the linear charge density of the conductor, and l is the length of the conductor.

## 3. Can the total induced charge of an infinite cylindrical conductor be negative?

Yes, the total induced charge of an infinite cylindrical conductor can be negative if the external electric field induces a flow of electrons in the opposite direction, resulting in a net negative charge on the conductor.

## 4. How does the shape of the conductor affect the total induced charge?

The shape of the conductor does not have an impact on the total induced charge, as long as the conductor is infinite in length. The total induced charge is solely dependent on the linear charge density and the length of the conductor.

## 5. Is the total induced charge the same for all points on the conductor?

No, the total induced charge may vary at different points along the conductor due to variations in the electric field strength or the linear charge density. However, the sum of all the induced charges at different points on the conductor will always equal the total induced charge of the conductor.