hw1_p5405_f06 - HW 1 Phys5405 F06 due Aug. 31 1) Given a...

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Unformatted text preview: HW 1 Phys5405 F06 due Aug. 31 1) Given a constant electric field, E = E0 ex . Write the field in cylindrical and spherical components and unit vectors. 2) What does (V · )r equal if V is an arbitrary vector? What is (V · r), if V is a constant vector? 3) Find the curl of a vector in spherical coordinates in the manner of the notes. Check your answer against the result in the text. In problems 4 and 5 A, B, F, G are all arbitrary vectors × (A × B) = A 4) Prove 5) Prove V dV ( · G + (G · ·B−B ))F = · A + (B · S )A − (A · )B daF(G · n), where S is the boundary area of volume V and n is the outward normal at surface element da. 1 ...
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