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Questions and Answers
What is the curl of a vector field?
What is the curl of a vector field?
- A scalar value that measures the magnitude of the vector field.
- A vector that represents the tendency of the vector field to rotate at a point. (correct)
- A scalar value that represents the divergence of the vector field.
- A vector that represents the gradient of the vector field.
What is the formula for calculating the curl of a vector field F = P i + Q j + R k in Cartesian coordinates?
What is the formula for calculating the curl of a vector field F = P i + Q j + R k in Cartesian coordinates?
- $dF/dt$
- $\nabla \times F$ (correct)
- $\nabla \cdot F$
- $ \nabla F$
What is the curl of the vector field F = 2xi + 3yj + 4zk in Cartesian coordinates?
What is the curl of the vector field F = 2xi + 3yj + 4zk in Cartesian coordinates?
- 0i + 0j + 0k (correct)
- 4i + 3j + 2k
- 0i + 4j + 3k
- 0i + 0j + 0k (correct)
What is the magnitude of the curl of a vector field?
What is the magnitude of the curl of a vector field?
Given the vector field F = 2xi + 3yj + 4zk, what is the magnitude of its curl?
Given the vector field F = 2xi + 3yj + 4zk, what is the magnitude of its curl?
Flashcards
Curl of a Vector Field
Curl of a Vector Field
A measure of the rotation of a vector field at a point.
Vector F = 2xi + 3yj + 4zk
Vector F = 2xi + 3yj + 4zk
A vector function comprising three components related to x, y, and z axes.
Magnitude
Magnitude
The length or size of a vector or scalar quantity.
Options for Curl's Magnitude
Options for Curl's Magnitude
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Calculating Curl
Calculating Curl
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Study Notes
Curl Magnitude Calculation
- The curl of vector F = 2xi + 3yj + 4zk is being calculated.
- The magnitude of the curl is asked for.
- The curl of a vector (in this case, F) is a vector operator that measures the rotation of the vector field.
- In this case, the rotation of vector F is zero because the vector components are independent of their position.
- The correct answer is 0.
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