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Solved Problems-2

Problems-2
  1. For a vector field Description: 83391.png, show explicitly that Description: 83381.png, i.e., the divergence of the curl of any vector field is zero.
  2. For a scalar field V, show that Description: 83371.png, i.e., the curl of the gradient of any scalar field is zero.
Solution
  1. Let, Description: 83364.png
     
    Description: 101099.png






     
    Description: 83344.png
    Description: 102809.png
  1. Description: 83328.png
     
    Description: 83321.png
    Description: 83314.png
     
 
Note: These two vector identities are known as null identities.




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