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Consider a vector field \( \vec{F} = (2xz + 3y^2)\hat{y} + 4yz^2\hat{z} \). The closed path (\( \Gamma \): \( A \rightarrow B \rightarrow C \rightarrow D \rightarrow A \)) in the \( z = 0 \) plane is shown in the figure.
\( \oint_\Gamma \vec{F} \cdot d\vec{l} \) denotes the line integral of \( \vec{F} \) along the closed path \( \Gamma \). Which of the following options is/are true?
Consider a vector field \( \vec{F} = (2xz + 3y^2)\hat{y} + 4yz^2\hat{z} \). The closed path (\( \Gamma \): \( A \rightarrow B \rightarrow C \rightarrow D \rightarrow A \)) in the \( z = 0 \) plane is shown in the figure.
\( \oint_\Gamma \vec{F} \cdot d\vec{l} \) denotes the line integral of \( \vec{F} \) along the closed path \( \Gamma \). Which of the following options is/are true?
\( \oint_\Gamma \vec{F} \cdot d\vec{l} \) denotes the line integral of \( \vec{F} \) along the closed path \( \Gamma \). Which of the following options is/are true?
Updated On: Jul 12, 2024
- \( \oint_\Gamma \vec{F} \cdot d\vec{l} = 0 \)
- \( \vec{F} \) is non-conservative.
- \(\vec{\nabla} \cdot \vec{F} = 0\)
- \(\vec{F}\) can be written as the gradient of a scalar field
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The Correct Option is A, B
Solution and Explanation
The correct Answers are (A):\( \oint_\Gamma \vec{F} \cdot d\vec{l} = 0 \),(B):\( \vec{F} \) is non-conservative.
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