# Electrostatics: Field and Potential

Please solve and show solutions step by step for problems 22.38, 22.42, and 23.68

(See attached files for full problem description)

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#### Solution Summary

Solutions of three problems good to learn basics.---------

(1) A point charge is placed at the center of a conducting charged spherical shell. The field at any point and is calculated with other questions in four parts of the question. -------------

(2) A solid conducting charged sphere surrounded by an insulating shell of radii a and b. The field at any point, charge density and other quantities are determined in three parts of the question. ------------

(3) A uniformly charged wire is bent in semicircular ring. the potential at the center of curvature is calculated.

Electrostatic Field and Potential in Spheres

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).

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