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Find the Laplace equation value of the following potential field
V = x2 – y2 + z2
V = x2 – y2 + z2
- a)0
- b)2
- c)4
- d)6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the Laplace equation value of the following potential fieldV = x2...
Answer: b
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation.
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation.
Most Upvoted Answer
Find the Laplace equation value of the following potential fieldV = x2...
Answer: b
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation.
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace equation.
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Community Answer
Find the Laplace equation value of the following potential fieldV = x2...
To find the Laplace equation value of the potential field V = x^2, we need to calculate the Laplacian of V.
The Laplacian operator is defined as the sum of second partial derivatives of a function with respect to each variable. In this case, we have a 2D potential field with only one variable, x.
The Laplacian of V can be calculated as follows:
∇^2V = ∂^2V/∂x^2
Taking the second partial derivative of V with respect to x:
∂^2V/∂x^2 = ∂/∂x (∂V/∂x)
Differentiating V = x^2 with respect to x:
∂V/∂x = 2x
Taking the derivative of 2x with respect to x:
∂^2V/∂x^2 = 2
Therefore, the Laplace equation value of the potential field V = x^2 is 2.
The Laplacian operator is defined as the sum of second partial derivatives of a function with respect to each variable. In this case, we have a 2D potential field with only one variable, x.
The Laplacian of V can be calculated as follows:
∇^2V = ∂^2V/∂x^2
Taking the second partial derivative of V with respect to x:
∂^2V/∂x^2 = ∂/∂x (∂V/∂x)
Differentiating V = x^2 with respect to x:
∂V/∂x = 2x
Taking the derivative of 2x with respect to x:
∂^2V/∂x^2 = 2
Therefore, the Laplace equation value of the potential field V = x^2 is 2.
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