3.9.[1] A uniform volume charge density of 80 µC/m3 is present throughout the region 8mm < r < 10mm. Let p, = 0 for 0 10 mm, find D, at r = 20 mm. 3.10.[1] A cube is defined by 1< x, y, z < 1.2. If D = 2x?y a, + 3x?y? a, C/m?: (a) apply Gauss's law to find the total flux leaving the closed surface of the cube; (b) evaluate ax at the center of the cube, (c) Estimate the total charge ду az enclosed within the cube by using Equation below. aD, aD: Charge enclosed in volume Av = ax x volume Av 3.11.[1] Let a vector field be given by G = 5x?y?z?ay. Evaluate both sides of Eq. aD, aD: ax x volume Av Charge enclosed in volume Au = For this G field and the volume defined by x = 3 and 3.1, y = 1 and 1.1, and z = 2 %3! and 2.1. Evaluate the partial derivatives at the center of the volume.

A very small sphere of mass 80 g having a charge q is held at a height of 9 m vertically above the centre of a fixed conducting sphere of radius 1 m, carrying an equal charge q. When released, it falls until it is repelled back just before it comes in contact with the sphere Calculate the charge q. [g = 10 m/s²]

[Numbers change] In the early 1900's Robert Millikan discovered the peculiar property that charge came in little packets, no smaller than e = 1.602 x 10-19 C -- he had measured the charge of the electron. Here's (roughly) how he did it. He removed an electron from an initially neutral droplet of oil with diameter 0.8 um. In a vacuum, he positioned the droplet between two metallic plates separated by 4 mm and fiddled with the potential (voltage) across the plates until the droplet would hover against the force of gravity. Droplets of this size with +e charge would hover, but only for a particular voltage (otherwise they would sink or rise). Given the parameters stated here, and the fact that the density of the oil was 815 kg/m³, what was the voltage that made the droplets hover? (give your answer with 0.1 V precision)

4.) Figure Q.2 (b) shows a cylindrical structure with length of 50 m. The inner and the outer surface are separated by free space and located at r = a and r = b respectively. The inner and outer surface of the structure contain a total charge of +1pC and -1pC, respectively. An infinitely long line charge with line charge density of +1pC/m is introduced along the axis of the structure. Given that a = 1 mm and b = 2 mm. +pa C/m? -Рь С/m? Figure Q.2(b) i. Calculate +pa and -pp at radius a and b respectively ii. Find D and E in all regions iii. Sketch graph |D| versus r