A very long, very thin straight line has a uniform charge per unit length of λ, where λ > 0. It is surrounded by a long, cylindrical, insulating rubber shell, which has an inner radius a and outer radius b. The line lies along the central axis of the cylindrical shell. The cylindrical shell has a uniform volume charge density ρ, where ρ > 0. (Both the line and the shell are long enough to approximate them as infinitely long.) Find the electric field in the following regions by choosing a gaussian cylinder of radius r and length L. (Use any variable or symbol stated above along with the following as necessary: ε .) (a)r < a magnitude E = direction ---Select--- (b)a < r < b magnitude E = direction ---Select--- (c)r > b magnitude E = direction ---Select---
A very long, very thin straight line has a uniform charge per unit length of λ, where λ > 0. It is surrounded by a long,
cylindrical, insulating rubber shell, which has an inner radius a and outer radius b. The line lies along the central axis of the
cylindrical shell. The cylindrical shell has a uniform volume charge density ρ, where ρ > 0. (Both the line and the shell are long
enough to approximate them as infinitely long.)
Find the electric field in the following regions by choosing a gaussian cylinder of radius r and length L. (Use any variable or
symbol stated above along with the following as necessary: ε .)
(a)r < a
magnitude E =
direction ---Select---
(b)a < r < b
magnitude E =
direction ---Select---
(c)r > b
magnitude E =
direction ---Select---
(d) What If? Suppose we have the same situation as described above, where again λ > 0, but now ρ can be any value. For
what value of ρ will there be zero electric field for r > b?
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