A vector field is given by, a(xj-yi) for (x* +y*)s¢(region-1} F(F)= (xj-yi) for (x' + y*) > r? (region -- I) X1- an (x*+y') Here a and r, are two constants. (a) Find the curl of this field both the regions. (b) Find the line integral OF.dl along the closed semicircle path of radius 2r, as shown in the figure below.
A vector field is given by, a(xj-yi) for (x* +y*)s¢(region-1} F(F)= (xj-yi) for (x' + y*) > r? (region -- I) X1- an (x*+y') Here a and r, are two constants. (a) Find the curl of this field both the regions. (b) Find the line integral OF.dl along the closed semicircle path of radius 2r, as shown in the figure below.
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Transcribed Image Text:A vector field is given by,
for (x² +y)<r (region-I)
F(f) =
ar
y*) > r; (region -- I)
for (x +
2
Here a and r, are two constants.
(a) Find the curl ofthis field both the regions.
(b) Find the line integral GF.dl along the closed semicircle path of radius 2r, as shown in the figure below.
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