1. The problem statement, all variables and given/known data
Good day everyone. I am studying Gaussian cylindrical surfaces. I have three questions:
(1) Books would say that the electric field lines would emanate from the lateral side of the cylinder and that the ends will not contribute anything. I cannot understand this because if I have a charged cylinder, I picture field lines to be emanating and perpendicular from the entire cylinder surface including the top and end part. Can you explain why are the ends not contributing to the flux ψ=∫E da? Wouldn't electric field lines parallel to da on top and end of cylinder (if there is such a thing) contribute to the total flux?
(2) I picture a thin disk (example is a coin) as a cylinder with a very small height. But when we get the electric field of such, we just assume that electric field emanates from the "face" of the disk and not from the sides. Why wouldn't field lines emanate also from the sides as it would do for ordinary cylinders? Wouldn't electric field lines leave charged solid volumes in the same way for same shape? Why why would electric field lines emanate differently for cylinders of varying thickness and height?
(3) Also, if you have a very large plane of charge. I was wondering why electric field lines wouldn't emanate from the fringes of the plane and parallel to the plane. I was thinking of the plane as a collection of smaller charges dq and that the electric field from each adjacent dq would cancel. But at the sides, there is none to cancel the E-field due to outermost dq so field lines from the edges should also contribute and point parallel to the plane.
2. Relevant equations
[itex] \int E \cdot da = \frac {q_{enc}}{ε_o} [/itex]
[itex] E = \int \frac {dq ~\hat{r}}{r^2} [/itex] where r is the vector from the source to the location of electric field.
3. The attempt at a solution
I think most of my thoughts are expressed in the question part. Thank you very much. :shy:
Good day everyone. I am studying Gaussian cylindrical surfaces. I have three questions:
(1) Books would say that the electric field lines would emanate from the lateral side of the cylinder and that the ends will not contribute anything. I cannot understand this because if I have a charged cylinder, I picture field lines to be emanating and perpendicular from the entire cylinder surface including the top and end part. Can you explain why are the ends not contributing to the flux ψ=∫E da? Wouldn't electric field lines parallel to da on top and end of cylinder (if there is such a thing) contribute to the total flux?
(2) I picture a thin disk (example is a coin) as a cylinder with a very small height. But when we get the electric field of such, we just assume that electric field emanates from the "face" of the disk and not from the sides. Why wouldn't field lines emanate also from the sides as it would do for ordinary cylinders? Wouldn't electric field lines leave charged solid volumes in the same way for same shape? Why why would electric field lines emanate differently for cylinders of varying thickness and height?
(3) Also, if you have a very large plane of charge. I was wondering why electric field lines wouldn't emanate from the fringes of the plane and parallel to the plane. I was thinking of the plane as a collection of smaller charges dq and that the electric field from each adjacent dq would cancel. But at the sides, there is none to cancel the E-field due to outermost dq so field lines from the edges should also contribute and point parallel to the plane.
2. Relevant equations
[itex] \int E \cdot da = \frac {q_{enc}}{ε_o} [/itex]
[itex] E = \int \frac {dq ~\hat{r}}{r^2} [/itex] where r is the vector from the source to the location of electric field.
3. The attempt at a solution
I think most of my thoughts are expressed in the question part. Thank you very much. :shy:
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