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Which of the following potentials does not satisfy Laplace's equation?

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BPSC AE Paper 5 (Electrical) 25 Mar 2022 Official Paper
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  1. V = 2x + 5
  3. V = 10xy
  4. V = ρ cosϕ

Answer (Detailed Solution Below)

Option 2 :
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Detailed Solution

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Concept:

The condition for potential (V) to satisfy Laplace's equation is given by:

Laplace equations in different coordinate systems are given by:

  • Cartesian System: 
  • Cylindrical System: 
  • Spherical System: 

​Calculation:

Option 1: V = 2x + 5

It satisfies the Laplace equation.

Option 2: 

 



It does not satisfy the Laplace equation.

Option 3: V = 10xy

It satisfies the Laplace equation.

Option 4: V = ρ cosϕ 

It satisfies the Laplace equation.

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