(a) Two metal objects are embedded in weakly conducting material of conductivity σ (Fig...

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(a) Two metal objects are embedded in weakly conducting material of conductivity σ (Fig XXXXXXXXXXShow that the resistance between them is related to the capacitance of the arrangement by

(b) Suppose you connected a battery between 1 and 2, and charged them up to a potential difference . If you then disconnect the battery, the charge will gradually leak off. Show that V (t) = , and find the time constant, r, in terms of ϵ_o and a.

Robert · Accepted Answer

Answer:
a)  
Suppose a charge Q is placed on the positively charged conductor. Enclose the positively 
charged conductor with a surface S. Then, the current flowing from the positively 
charged conductor is equal to 
surface
I J da   
Where the surface integral is taken over a surface that encloses the positively charged 
conductor (for example, the dashed surface in Figure 7.6). The expression for I can be 
rewritten in terms of the electric field as,

(a) Two metal objects are embedded in weakly conducting material of conductivity σ (Fig XXXXXXXXXXShow that the resistance between them is related to the capacitance of the arrangement by (b) Suppose...

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