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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


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.


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


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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