Let A be given in a spherical coordinate system. Use eq. 3.64 and prove that the...

 

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Let A be given in a spherical coordinate system. Use eq. 3.64 and prove that the three spherical components of V2A can be expressed as 2A, (V²A), = V²A, - 24- (V²A), = V²A, + (V²A) = V²A - - 2 JA, ae 2 JA : - 20 cot 0 — 7 sin 0 2A, 2 ae A rsin¹0 r² Ap sin²0 cos 8 A 2 r² sine ad aA + ad 2 JA, 2 cos @ A rsin e ad rsin¹0 ao Let A be given in a spherical coordinate system. Use eq. 3.64 and prove that the three spherical components of V2A can be expressed as 2A, (V²A), = V²A, - 24- (V²A), = V²A, + (V²A) = V²A - - 2 JA, ae 2 JA : - 20 cot 0 — 7 sin 0 2A, 2 ae A rsin¹0 r² Ap sin²0 cos 8 A 2 r² sine ad aA + ad 2 JA, 2 cos @ A rsin e ad rsin¹0 ao