Consider a one-dimensional scalar field f(x) = A (2x -) defined for -1 sxs1where x is the gauge length. Calculate the effective measurand, f, if the sensing gauge length is -0.5 sxs 1. 05

Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.

For multipole expansion, under what conditions, if any, is it an exact expression, and under what conditions, if any, is it an approximation? In what limits/cases is it the most useful?

Problem An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is 38 312 where Bis a constant and ris the distance from the center of the sphere. What is electric field at any point inside the sphere? Solution To find the electric field inside the non-uniformly charged sphere, we may apply integration method or the Gauss's Law method. Here, let us use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface of a sphere, then evaluate the dot product to obcain (Equation 1) The issue however is how much charge does the Gaussian surface encoses? Since, our sphere is an insulating material. charges will get distributed non-uniformly within the volume of the object. So, we look into the definition of volume charge density to find the enclosed charge. So, we have dq p= dv Based on the given problem, we can also say that dgenc p= 38 dV