The figure shows four pairs of parallel identical conducting plates, separated by the same distance 2.0 cm and arranged perpendicular to x -axis. The…

The figure shows four pairs of parallel identical conducting plates, separated by the same distance $\displaystyle 2.0$ cm and arranged perpendicular to x -axis. The electric potential of each plate is mentioned. The electric field between a pair of plates is uniform and normal to the plates.

For which pair of the plates is the electric field $\displaystyle \overrightarrow{\mathrm{E}}$ along $\displaystyle \hat{\mathrm{i}}$ ?

I (B) II

III

IV

An electron is released midway between the plates of pair IV. It will :

move along $\displaystyle \hat{\mathrm{i}}$ at constant speed

move along $\displaystyle -\hat{\mathrm{i}}$ at constant speed

accelerate along $\displaystyle \hat{\mathrm{i}}$

accelerate along $\displaystyle -\hat{\mathrm{i}}$

Let $\displaystyle \mathrm{V}_{0}$ be the potential at the left plate of any set, taken to be at $\displaystyle \mathrm{x}=0 \mathrm{~m}$. Then potential V at any point $\displaystyle (0 \leq \mathrm{x} \leq 2 \mathrm{~cm})$ between the plates of that set can be expressed as :

$\displaystyle \mathrm{V}=\mathrm{V}_{0}+\alpha \mathrm{x}$

$\displaystyle \mathrm{V}=\mathrm{V}_{0}+\alpha \mathrm{x}^{2}$

$\displaystyle \mathrm{V}=\mathrm{V}_{0}+\alpha \mathrm{x}^{1 / 2}$

$\displaystyle \mathrm{V}=\mathrm{V}_{0}+\alpha \mathrm{x}^{3 / 2}$ where $\displaystyle \alpha$ is a constant, positive or negative.