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Verify whether the following functions are valid potential functions.
(i) ϕ = A(X− Y2)
(ii) ϕ = Acos x
  • a)
    Both are valid potential functions
  • b)
    Both are not valid potential functions
  • c)
    (i) Is not a valid function (ii) Is a valid potential function
  • d)
    (i) Is a valid potential function (ii) Not a valid function
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Verify whether the following functions are valid potential functions.(...
The given potential function is ϕ(x) = A(x^2), where A is a constant.

To verify if this is a valid potential function, we need to check if its gradient satisfies the condition ∇ϕ = F, where F is the given vector field.

Taking the gradient of ϕ(x) = A(x^2), we have:
∇ϕ = 2Ax

Now, we need to compare this with the given vector field F. If F = 2Ax, then ϕ(x) is a valid potential function.

If F is not equal to 2Ax, then ϕ(x) is not a valid potential function.

Therefore, without the given vector field, we cannot determine if ϕ(x) = A(x^2) is a valid potential function.
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Community Answer
Verify whether the following functions are valid potential functions.(...
Properties of Potential functions:
1. If velocity potential (ϕ) exists, the flow should be irrotational.
2. If velocity potential (ϕ) satisfies the Laplace equation, it represents the possible steady incompressible irrotational flow.
Calculation:
Given:

(i) ϕ = A(X2 − Y2), (ii) ϕ = Acos x.
(i) ϕ = A(X2 − Y2),

(ii) ϕ = Acos x

Thus (i) is a valid potential function as it satisfies the Laplace equation, whereas (ii) is not a valid potential function as it does not satisfy Laplace equation.
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Verify whether the following functions are valid potential functions.(i) = A(X2− Y2)(ii) = Acos xa)Both are valid potential functionsb)Both are not valid potential functionsc)(i) Is not a valid function (ii) Is a valid potential functiond)(i) Is a valid potential function (ii) Not a valid functionCorrect answer is option 'D'. Can you explain this answer?
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