Express the vector field D = (x² + y²)−¹(xɑx + yay) in cylindrical components and cylindrical variables. (b) Evaluate D at the point where p = 2, p = 0.2, and z=5, expressing the result in cylindrical and rectangular components.

Express the vector field D = (x² + y²)−¹(xɑx + yay) in cylindrical components and cylindrical variables. (b) Evaluate D at the point where p = 2, p = 0.2, and z=5, expressing the result in cylindrical and rectangular components.

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Question

Express the vector field D = (x² + y²)-¹(xax +ya,) in cylindrical components and
cylindrical variables. (b) Evaluate D at the point where p = 2,4 = 0.2π, and z=5,
expressing the result in cylindrical and rectangular components.

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Step 1: Know the relation between the cartesian and cylindrical components of a vector:

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Step 2: (a) Express the given vector field in cylindrical coordinate system:

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Step 3: (b) Calculate the vector field at the given point in cylindrical coordinate system:

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Step 4: (b) Calculate the vector field at the given point in cartesian coordinate system:

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