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Solved Problem-2

Problem-2
Find the potential and electric field intensity for the region between two concentric right circular cylinders, where V = 0 at ra = 1 mm and V = 100 V at rb = 20 mm. Neglect fringing.
Solution
Since V varies with r only, Laplace’s equation can be written as,
Description: 169671.png
 
Integrating twice,
Description: 169664.png
 
where, A and B are constants.
 
Applying boundary conditions, we get,
 
At r = ra = 0.001, V = 0 ⇒ 0 = A ln(0.001) + B
 
At r = rb = 0.02, V = 100 ⇒ 100 = A ln(0.02) + B
 
Solving, A = 33.36 and B = 230.49
Description: 169656.png
 
Hence, the field intensity is given as,
Description: 169648.png
 





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