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Homework Statement
Charge is uniformly distributed along the x-axis with density ß. Use Gauss' Law to find the electric field it produces, and use this to calculate the work done on a charge Q that moves along the y-axis from y = a to y = b.
Homework Equations
[itex]\phi[/itex]=[itex]\int[/itex][itex]\vec{E}[/itex]*[itex]\hat{n}[/itex]dA
[itex]\phi[/itex]= [itex]\frac{Q}{\epsilon}[/itex]
The Attempt at a Solution
I used a cylinder for my surface since the normal vector will always align with the electrical field. So the first part, the equation ends up
[itex]\phi[/itex]=E[itex]\int[/itex]dA
[itex]\phi[/itex]=E(2∏rh)
(r is the radius from the axis to the edge of the cylinder and h is the length of the cylinder.)
and if I remember right, Q is the density times the are of enclosure.
so Q = β(2∏rh)
I set the two [itex]\phi[/itex] equations equal to each other and get
[itex]\frac{β}{ε}[/itex]=E
I don't think that's right though. What did I do wrong?
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