See the attached file.
1. The electrostatic field E in a particular region can be expressed in terms of spherical coordinates. Derive an expression for the potential difference.
2. The electrostatic potential in a region is given by a function. Derive an expression for the electrostatic field in this region, and hence determine the field at the point x = 1.0m, y = 2.0m, z = 3.0m. Enter the numerical values for the components of this field in the boxes in the equation below:
3. A cube of volume L^3 is bounded by the planes x = 0 and x = L, y = 0 and y = L, and z = 0 and z = L. he charge density p(x) within the cube is given by and equation. Calculate the total charge contained within the cube.
4. The region between two concentric spheres of radi alpha and 3*alpha contains a uniform charge density p and elsewhere the charge density is zero. Calculate the radial component of the electric field a a distance 2a from the centre of the spheres, E(2a).
See attachments for full solutions.
Question 1: For spherical coordinate system we may choose a path such that the field remains parallel to the path everywhere. Such path will have one part along the arc of angle ?? of radius r1, than along the radius from r1 ...
The solution examines electrostatic fields and potential in spheres.