# Electric field varies with r

## Homework Statement

based on the diagram attached, find the electric field E that varies with r.
the line and the metallic cylindrical shell are infinitely long.
the outer radius of the cylindrical shell is b and the inner one is a
and the line charge density for the line is $$\lambda$$
and the line charge density for the cylindrical shell is $$\lambda$$s

## Homework Equations

Gauss's Law ( $$\oint$$E dA = Qin / $$\epsilon$$

## The Attempt at a Solution

by using gauss's law with cylindrical gaussian surface coaxial with the line,
when r < a, i have E = $$\lambda$$ / (2*pi*$$\epsilon$$*r);
for a< r < b, i have E = 0 since the shell is a conductor;

but for r > b, is it E = ($$\lambda$$s + $$\lambda$$) / (2*pi*$$\epsilon$$*r) since the total charge enclosed is the sum of charges in the two bodies?

Pls help me. thanks

#### Attachments

• pap112tut1-2.jpg
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## Answers and Replies

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Your calculations are correct.