(a) In a certain region of space, the volume charge density ? has a uniform positive value. Can be uniform in this region? Explain. (b) Suppose that in this region of uniform positive ? there is a “bubble” within which ? = 0. Can be uniform within this bubble? Explain.
Solution 15DQ Step 1 of 3: (a) In a certain region of space, the volume charge density has a uniform positive value. Can be uniform in this region Explain. The electric field lines of a uniform electric field are equally spaced in same direction. Thus, if we place any closed surface in such a region of uniform electric field, the net electric flux through the surface will be zero. As flux depends on field lines, the number of lines entering the closed surface is equal to the number of field lines leaving the surface. Step 2 of 3: From Gauss’s law we know that, electric flux through a closed surface is directly proportional to the charge enclosed by the surface. In the given case as the electric flux is zero, there is zero charge enclosed by the surface. Therefore, the electric field cannot be uniform in a given region if there is some net charge or charge density in the same region.