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A cubical box (sides of length a) consists of five metal

Chapter 3, Problem 16P

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QUESTION:

Problem 16P

A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig. 3.23). The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential V0. Find the potential inside the box. [What should the potential at the center (a/2, a/2, a/2) be? Check numerically that your formula is consistent with this value.]11

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QUESTION:

Problem 16P

A cubical box (sides of length a) consists of five metal plates, which are welded together and grounded (Fig. 3.23). The top is made of a separate sheet of metal, insulated from the others, and held at a constant potential V0. Find the potential inside the box. [What should the potential at the center (a/2, a/2, a/2) be? Check numerically that your formula is consistent with this value.]11

ANSWER:

Solution 16P

Step 1 of 7:

Consider a cubical box of side length  which consist of five metal plates welded together and grounded. We need to find out the potential  inside the box.

                        

The boundary conditions are,

  1. ,  
  2. ,  
  3. ,  
  4. ,  
  5. ,  
  6. ,  

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