If W = + i represents the complex potential for an electric field. Given = x^2 - y^2 + xx^2 + y^2, then the function is

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Complex Variable

If $${\text{W}} = \phi + {\text{i}}\psi $$ represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$ then the function $$\phi $$ is

A) $$ - 2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$ B) $$2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$ C) $$ - 2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$ D) $$2{\text{xy}} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

Answer & Solution

Correct Answer: Option A

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If text W = phi + text i psi &nbsp represents...

If $${\text{W}} = \phi + {\text{i}}\psi $$ represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$ then the function $$\phi $$ is

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