# 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

$$b = 10 V/s$$

$$l = 1 mm$$

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

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

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