In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.

Heat flow Electrostatics
$T( r )$ $V( r )$
$j ( r )$ $E ( r )$

We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is

  • [KVPY 2018]
  • A

    $2$

  • B

    $1$

  • C

    $-1$

  • D

    $-2$

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