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Two long, straight copper pipes, each of radius a, are

Chapter 7, Problem 41P

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QUESTION:

Problem 41P

Two long, straight copper pipes, each of radius a, are held a distance 2d apart (see Fig. 7.50). One is at potential V0, the other at −V0. The space surrounding the pipes is filled with weakly conducting material of conductivity σ. Find the current per unit length that flows from one pipe to the other. [Hint: Refer to Prob. 3.12.]

Figure 7.50

Reference prob 3.12

Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V0, the other at −V0 (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob. 2.52.]

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QUESTION:

Problem 41P

Two long, straight copper pipes, each of radius a, are held a distance 2d apart (see Fig. 7.50). One is at potential V0, the other at −V0. The space surrounding the pipes is filled with weakly conducting material of conductivity σ. Find the current per unit length that flows from one pipe to the other. [Hint: Refer to Prob. 3.12.]

Figure 7.50

Reference prob 3.12

Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V0, the other at −V0 (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob. 2.52.]

ANSWER:

Step 1 of 4

We have to find the current per unit length that flows from one copper  pipe to the other, each of radius and held at a distance apart.

To solve this problem, let us begin by solving a different problem of two parallel wires carrying charges and as shown in figure below.

7.41.PNG

The electric field and the potential due to one wire is,

where,  is the distance from the line charge to a point

             which is at a potential

             and are the distances from the line charge and to the

             point () respectively

Therefore, the potential due to the combination of two wires is,

where,  is distance from the origin to line charge.

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