Letr = (x + y)/2 and consider the vector field F = r(-yi+xj), where r #0...

 

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Letr = (x² + y²)¹/2 and consider the vector field F = r¹(-yi+xj), where r #0 and A is a constant. F has no z-component and is independent of (a) Find curl (14(-yi+x)), and show that it can be written in the form Tªk, where a = curl F = for any constant A. (b) Using your answer to part (a), find the direction of the curl of the vector fields with each of the following values of A (enter your answer as a unit vector in the direction of the curl): A = -6: direction = A = -1: direction = (c) For each values of A in part (b), what (if anything) does your answer to part (b) tell you about the sign of the circulation around a small circle oriented counterclockwise when viewed from above, and centered at (1, 1, 1)? If A = -6, the circulation is ? If A = -1, the circulation is ? Letr = (x² + y²)¹/2 and consider the vector field F = r¹(-yi+xj), where r #0 and A is a constant. F has no z-component and is independent of (a) Find curl (14(-yi+x)), and show that it can be written in the form Tªk, where a = curl F = for any constant A. (b) Using your answer to part (a), find the direction of the curl of the vector fields with each of the following values of A (enter your answer as a unit vector in the direction of the curl): A = -6: direction = A = -1: direction = (c) For each values of A in part (b), what (if anything) does your answer to part (b) tell you about the sign of the circulation around a small circle oriented counterclockwise when viewed from above, and centered at (1, 1, 1)? If A = -6, the circulation is ? If A = -1, the circulation is ?

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a To find the curl of the vector field F rAyizj we can use the formula for curl in Cartesian coordin... View the full answer