Question
At a particular point in a material with resistivity $\rho$ the current density has magnitude $J$. Show that the power per unit volume dissipated at this point is $J^{2} \rho$.
Step 1
First, we need to recall the relationship between current density (J), resistivity (ρ), and electric field (E). According to Ohm's law, we have: J = σE, where σ is the conductivity, which is the reciprocal of resistivity (ρ): σ = 1/ρ. So, E = Jρ. Show more…
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At a particular point in a material with resistivity $\rho$ the current density has magnitude $J .$ Show that the power per unit volume dissipated at this point is $J^{2} \rho.$
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