Question

An infinitely long cylindrical conducting shell of outer radius r=0.10 m and inner radius ry=008 m initially carries a surface charge density o=0.15 µC/m². A thin wire, with linear charge density & Chm, is inserted along the shells axis. The shell and the wire do not touch and there is no charge exchanged between them.

>&315 Part) What is the new surface charge density, in microcoulombs per square meter, on the inner surface of the cylindrical shell?

Answer 1

Answer:

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Answer 2

Given:

the outer radius of the shell ($r_{1}$) is 0.10m

the inner radius ($r_{2}$) = 0.08m

surface charge density (σ) = 0.15μC/$m^{2}$

linear charge density (λ)      = 1.1μC/m

To find: the new charge density, in micro coulombs per square meter, on the outer surface of the cylindrical shell.

Explanation:

Before the wire is inserted, the total charge on the inner and outer surface of the cylindrical shell is as follows,

                                $Q_{in}$ = σ($2\pi r_{1} h$)

                                      = $(-0.35)(2\pi (0.08)h)$

                                      = $-0.175h$μ$C$

                               $Q_{in}$ = σ($2\pi r_{2} h$)

                                      = $(-0.35)(2\pi (0.1)h)$

                                     =$-0.22h$μ$C$

Here, 'h' denotes the length of the cylinder. The total charge of the cylindrical shell is -0.395h μC.

When the thin wire is inserted, the positive charge of the wire attracts the same amount of negative charge on the inner surface of the shell.

                    $Q_{wire}$ = λh

                             = 1.1hμC

a) The new charge on the inner shell is -1.1h µC. Therefore, the new surface charge density of the inner shell can be calculated as follows:

                        σ2 = $\frac{Q_{in} }{2\pi r_{1} h}$

                              =$\frac{-1.1h}{2\pi r_{1}h }$

                              = $\frac{-1.1}{2\pi (0.08)}$

                             = $-2.18$μ$C/m^{2}$

hence the new charge density, in micro coulombs per square meter, on the outer surface of the cylindrical shell is -2.18μ$C/m^{2}$