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Solved Problems-7

Problem-7
(a) Determine the constant c such that the vector Description: 82518.png will be solenoidal.
(b) Find the value of the constant Q to make Description: 82509.png, solenoidal.
(c) Find the constants a, b, c so that the vector, Description: 82499.png is irrotational.
Solution
(a) Description: 82490.png
The vector will be solenoidal if its divergence is zero.
 Description: 82481.png

(b) Description: 82474.png 
The vector will be solenoidal if its divergence is zero.
 Description: 82467.png

(c) Description: 82459.png 
The vector will be irrotational if its curl is zero.
 Description: 82452.png
This vector will be zero if and only if its components are individually zero.
Description: 82445.png
and
Hence, a = 4, b = 2, c = -1.
 





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