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Update: The answer is 120 degrees using the angles between all the axis x = cos^-1 (+/- sqrt(1-cos^2(y)-cos^2(z)) x = cos^-1(+/- 0.493) x = 60 or 120

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The angles given give you 2 out of 3 of the direction cosines, namely $\gamma_y$ and $\gamma_z$. What relationship do the three direction cosines $\gamma_x$, $\gamma_y$ and $\gamma_z$ fulfill? Recall that they are the components of a unit vector, since they are the lengths of the projection onto the three axes of a unit vector pointing along the boom.

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The volume element is $(dr)*(rd \phi)*(dz)$. Hence, the extra r in your integrand should be eliminated.

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Charge, giving rise to EM fields (or any other kind of field, really) does create spacetime curvature. See for instance the difference between the Schwarzschild metric and the Reissner-Nordström metric.

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