Imagine a closed surface S made up of two cylinders, one of radius a and one of
ID: 3077046 • Letter: I
Question
Imagine a closed surface S made up of two cylinders, one of radius a and one of larger radius b, both coaxial with the wire, and the two washers that cap the ends. The outward orientation of S means that a normal on the outer cylinder points away from the wire and a normal on the inner cylinder points toward the wire.(i) Explain why the flux of E-->, the electric field, through the washers is 0.
(ii) Explain why Gauss's Law implies that the flux through the inner cylinder is the same as the flux through the outer cylinder. [Hint: the charge on the wire is not inside the surface S]
(iii) use part (ii) to show that E_b / E_a = a / b
(iv) Explain why part (iii) shows that the strength of the field due to an infinitely long uniformly charged wire is proportional to 1 / r.
Explanation / Answer
Imagine a closed surface S made up of two cylinders, one of radius a and one of larger radius b, both coaxial with the wire, and the two washers that cap the ends. (See Figure 19.33.) The outward orientation of S means that a normal on the outer cylinder points away from the wire and a normal on the inner cylinder points toward the wire. (i) Explain why the flux of E? , the electric field, through the washers is 0. (ii)