Some questions on Special and Newtonian Relativity

[maverick280857]

Homework Statement

Question 1: Is Ohm's Law (V = IR) invariant under Galilean transformations?
Question 2: Model the Earth as an ellipsoid or a spheroid, and find the lowest order correction to the inverse square law at points inside and outside the Earth's surface.

Homework Equations

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The Attempt at a Solution

Question 1: Using the low velocity regime of the Lorentz transformations, we see that j = j', E = E' and so

[tex]j = \sigma E[/itex]<br /> <br /> is invariant in both reference frames. As lengths are invariant under a Galilean transformation, this is equivalent to V = IR in all inertial frames. Is this correct?<br /> <br /> Can this be argued <i>without</i> using the Lorentz transformations, i.e. without treating Galilean transformations as a special case of the Lorentz transformation for $v << c$?<br /> <br /> (Also, can resistivity or conductivity be regarded as a Lorentz invariant scalar?)<br /> <br /> <b>Question 2</b>: This has me stumped right now...I don't understand what has to be done here. I would appreciate if someone could point me in the right direction.[/tex]

 

[maverick280857]

Question 2: This has me stumped right now...I don't understand what has to be done here. I would appreciate if someone could point me in the right direction.

Anyone?