Charge density of a cylindrical shell

Electricity and Magnetism Level 3

Suppose that there are an infinitely long straight current-carrying wire and a thin cylindrical shell enveloping it. The linear charge density of the current-carrying wire is $-3.6 \text{ nC/m},$ and the radius of the cylindrical shell is $1.5 \text{ cm}$ . If the shell has a certain positive surface charge density $d$ such that the net electric field intensity of the outside of the shell is zero, what is the value of $d?$

1.9 \text{ nC/m}^2

38.2 \text{ nC/m}^2

3.6 \text{ nC/m}^2

7.2 \text{ nC/m}^2

1 solution

Chew-Seong Cheong
Aug 13, 2014

For the net electric field intensity of the outside of the cylindrical shell to be zero, a same amount charge is induced on the internal surface of the cylindrical shell per length of the infinitely long straight wire.

Let the charge of $1$ m of wire be $Q$ and the internal area of $1$ m length of the shell be $A$ , then we have:

$d = \cfrac{Q}{A}=\cfrac{3.6}{2\pi (0.015)(1)}=\boxed{38.2\space nC/m^2}$

Charge density of a cylindrical shell

1 solution

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