prob2 - A = A dx , compute F = dA and show that its...

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A.V. Manohar Ph225A: General Relativity Problem Set 2 1. You are given a vector feld ( A x ,A y ,A z ) in Cartesian coordinates. Compute ( A r ,A θ ,A φ ) and ( A r ,A θ ,A φ ) in spherical polar coordinates. 2. Convert the one-Form ω = x dy - y dx to polar coordinates. Compute d ω in both coordinate systems, and veriFy that the polar coordinate result is the same as converting the Cartesian d ω . 3. Given a Function f = r cos θ , compute dF and ddF. 4. Given a one-Form vector potential
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Unformatted text preview: A = A dx , compute F = dA and show that its components are the electric magnetic felds. Compute d (without assuming F = dA), and show that d = 0 are the source-Free Maxwell equations. 5. Let = sin d . VeriFy Stokes theorem i M d = i M where M is the Northern hemisphere oF a unit sphere. Repeat For = cos d . Why does Stokes theorem Fail in this case? 1...
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This note was uploaded on 04/19/2008 for the course PHYS 225 taught by Professor Manohar during the Fall '07 term at UCSD.

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