# Time varying Voltage

**Electricity and Magnetism**Level 4

At the moment \(t=0\), an electron leaves one plate of a parallel plate capacitor with a negligible velocity. An accelerating voltage varying as \(V = bt\), where \(b\) is constant, is applied between the plates. The separation between the plates is \(l\). Let the time taken by the electron to reach the opposite plate be \(t_0\) in microseconds.

What is

\(\large \lfloor t_0 \rfloor \ ? \)

**Details and Assumptions**

\(b = 10 V/s \)

\(l = 1 mm \)

\(e = 1.6 \times 10^{-19} \rightarrow \text{charge on electron}\)

\(m = 9.1 \times 10^{-31} \rightarrow \text{mass of electron}\)