# Relation between Temperature and heat current

This problem:

I was able to solve it doing this:

But I think i have nowhere " exploited " the equivalence given above. How can this be used in this problem?

• i guess you did "exploit' that equivalence when you wrote the first line of your solution. – Carrick Feb 8 at 7:22
• got it and put it in the answer – Starboy Feb 8 at 11:03

$$\frac {dQ}{dt} = j(\vec r)*4\pi r^2$$ Putting $$\frac {dT}{dr} =k* j(\vec r)$$ Since $$\frac {dV}{dr} = \vec E(\vec r)$$