# 3. Consider a vortex filament of strength  in the shape of a closed circular loop of radius R. Obtain an expression for the velocity induced at the center of the loop in terms of  and R, no other variables. Tip: Draw the loop on your page. If the vortices on the filament curve inward over the top of the loop, then the velocity vector points into the page, and vice-versa. Draw your vectors (dl and r) clearly to ensure you get the sign of the velocity vector correct. Your result will be a vector

###### Question:

3. Consider a vortex filament of strength  in the shape of a closed circular loop of radius R. Obtain an expression for the velocity induced at the center of the loop in terms of  and R, no other variables. Tip: Draw the loop on your page. If the vortices on the filament curve inward over the top of the loop, then the velocity vector points into the page, and vice-versa. Draw your vectors (dl and r) clearly to ensure you get the sign of the velocity vector correct. Your result will be a vector

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