Question

What is E(r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance r from the axis of the cylindrical rod?

Answer 1

The value of E(r) will be "$\frac{\lambda}{ 2 \pi \varepsilon_0 r}$".

According to the question,

• A conducting cylindrical shell surrounds an infinite long conducting cylindrical rod with something like a positive (+) charge.

By using Gauss law,

→ $E(r)\ \phi \ dA = \frac{q}{\varepsilon_0}$

or,

→ $E(r) (2 \pi r L) = \frac{q}{\varepsilon_0}$

           $E(r) = \frac{1}{2 \pi r \varepsilon_0} (\frac{q}{L} )$

           $E(r) = \frac{\lambda}{2 \pi \varepsilon_0 r}$

Thus the approach above is appropriate.          

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