Question

Calculate the value of the vector current density :

(a)in rectangular coordinates at P_A(2,3,4) if H = x²z a_y - y²x a_z

(b)in cylindrical coordiantes at P_B(1.5, 90deg, 0.5) if H = 2/ρ (cos 0.2φ) a_φ

(c)in spherical coordinates at P_c(2, 30deg, 20deg) if H = 1/(sinθ) a_θ

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Answer 1

J=vector current density

(a)        For rectangular see Curl(H) =
            when applying curl(H) we get
            J=(-2yx -2xz)ax  +   (2xz) az   +  (0-(-y²))ay

             therefore for points (2,3,4)  in the above equation we get
             J=-16ax + 9ay + 16az

 

(b)         For cylindrical see curl (H) =

             when applying curl(H) we get 
                

 

            Then
               

              now we insert the points (1.5,90^o, 0.5) and we get

              J=0.055az 

 

 

(c)         For spherical see Curl(H) =
             when applying curl(H) we get 
             

              then 

                

                

               now inserting point ( 2 , 30^o , 20^o) 
               we get  

               J=aφ