- #1
Karol
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Homework Statement
I have to prove that the electric field round a long conductive round bar of radius R is equal to that of a long thin wire, meaning the charge is on the center line
Homework Equations
The Gauss theorem:
##E\times A=q##
Where A is the area of the surface and q is the charge enclosed in it
The Attempt at a Solution
To find the field E when the charge is concentrated on the axis i take a round long volume with radius r:
##E\times 2\pi rl=\lambda l\rightarrow E=\frac{\lambda}{2\pi r}##
Where [itex]\lambda[/itex] is the charge per unit length.
The field near a round bar:
##E\times 2\pi rl=\sigma\cdot 2\pi R l##
Where [itex]\sigma[/itex] is the charge per unit surface, since the charge is concentrated only on the surface.
But [itex]\sigma\cdot 2\pi R l=\lambda l[/itex]
They both are the charge per unit length. and so is if i use the charge per unit mass.
I feel uncomfortable