Question #43427

An electron of mass $m$ (in $\text{kg}$) and charge $-e$ (in $\text{C}$) is constrained to move along a microscopic circular metallic ring of radius $R$ (in $\text{m}$). The ring is initially at temperature $T_0$ (in $\text{K}$) and has a coefficient of linear thermal expansion $\alpha$ (in $\text{K}^{-1}$). The electron is in the $n$-th stationary state, satisfying Bohr's angular momentum quantization condition. If the temperature of the ring is increased by a small amount $\Delta T$ (in $\text{K}$, such that $\alpha \Delta T \ll 1$), and the electron remains in the same $n$-th quantum state, which of the following correctly gives the fractional change in its orbital magnetic moment $\left(\frac{\Delta \mu}{\mu}\right)$ and the fractional change in its equivalent orbital current $\left(\frac{\Delta I}{I}\right)$?