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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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- Spring '10