![]() Once we substitute that straight in for Ar the integral looks longer but we've removed the dependence inside the integrand, so we can do the integration in a straight forward way. $$Ar = sinthetacosphicdot Ax + sinthetasinphicdot Ay + costhetacdot Az$$ The integral is over phi and theta but also dependent on phi and theta, therefore it's much easier to do this by switching back to cartesian coordinates by the relation: Where $Ar$ is a unit vector in the radial direction. Need to do an integration of $int( r^3cosphisinthetacdot Ar) dtheta dphi$ For example (using a textbook, Engineering Electromagnetics by Demarest. However the matrix you've found is for mapping a vector between the co-ordinate systems. ![]() For example, Matt Nagel, though quadriplegic, can use the 96 electrodes implanted into his motor cortex to move a cursor on a computer screen or. ![]() For a simple co-ordinate switch you can just use the relations: We won't neglect the truly implantable devices. This is not the Matrix you're looking for.
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