Question

Help with question 2

1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density. Let's make Pl = 2/y (Coulombs/metre). To make it easier for us to mark, line up this line of charge along the y-axis, going from y -0 to y- L 2. Derive an equation that represents the electric field at any point P that is located along the z-axis (0,0,2). For this question, you will notice that the x-component of the electric field is zero, but that there is both a y-component and a z-component. Solve the integral for the y-component. As for the z-component, just write the proper integral but you don't have to solve it. [In order to get points for this question, you must (1) include a schematic showing the described geometry; (2) identify the relevant integral equation, (3) clearly state the values ofF,F', dl',etc. and (4) solve the integral for the y-component. Use rectangular coordinates.] a. 3. Calculate the electric flux produced by D (459302) m2 through a . This cylindrical surface defined by 0 < z < 5 m , -0.5 m and 0 < ф < is not a closed surface (only consider the curve surface).

Answer 1

Apply gauss law integral E dA = q_en/E_0 E 2 pi r L = 2 ln L/E_0 E = ln(L)/pi r L E_0 q_eb = integral^L_0 2/y dy = 2 ln L r = distance from line charge