A circular cylindrical material having radius b has the polarization density where is a given…

A circular cylindrical material having radius b has the polarization density 330b196a 3436 4cd7 9dd0 98d96d9e07dd where 85196ed1 74a6 4a76 9bf9 d4ed19c928c4is a given positive integer. The region 703e607f b8a3 49ca 9721 52febf9480a1, shown in Fig. P6.3.9, is free space.

Fig P6.3.9

4f53140a a39a 439a ba64 e427042cc206

(a) Determine the volume and surface polarization charge densities for the circular cylinder.

(b) Find the potential in regions (a) and (b).

(c) Now the cylinder rotates with the constant angular velocity Ω. Argue that the resulting potential is obtained by replacing φ → (φ 0b7e01c3 b801 4491 85ef 7be58f6d8b3e).

(d) A section of the outer cylinder is electrically isolated and connected to ground through a resistance R. This resistance is low enough so that, as far as the potential in the gap is concerned, the potential of the segment can still be taken as zero. However, as the rotor rotates, the charge induced on the segment is time varying. As a result, there is a current through the resistor and hence an output signal 99611681 220b 4a51 8ad3 4d91dd1d60db. Assume that the segment subtends an angle 5a79bb10 e9af 4a37 8025 ab907b13d5ae and has length a499f199 9f91 455e abab f774b83c3b8b in the fc0dc90f ae13 4cc7 b837 c24303c935a1 direction, and find 99611681 220b 4a51 8ad3 4d91dd1d60db.

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