# Electron's refraction

**Electricity and Magnetism**Level 4

An electron with kinetic energy \(K=5~\textrm{eV}\) moves in a region with constant potential \(V_{1}=3~\textrm{V}\). The electron strikes a flat thin wall at \(\alpha=45^{\circ} \) (measured with respect to the normal) and emerges in a different region with constant potential \( V_{2}=2~\textrm{V}\). As a result, the electron refracts. Find the direction \(\beta\) **in degrees** of the electron's velocity (measured with respect to the normal) in the second region. Assume that the total energy of the electron is conserved as it passes though the wall.

Hint: You may model the thin wall as a parallel plate capacitor.

**Details and assumptions**

\(1~\textrm{eV}= 1.6 \times 10^{-19}~\textrm{C} \cdot\textrm{ V}\).