Relation Between Electric Field and Potential

A uniform field of $2.0 \mathrm{N} {\mathrm{C}}^{-1}$ exists in space in $\mathrm{x}$ direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point $(\mathrm{x}, \mathrm{y}, \mathrm{z})$. (b) At which points, the potential is $25 \mathrm{V}$? (c) If the potential at the origin is taken to be $100 \mathrm{V}$, what will be the expression for the potential at a general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?

An electric field of magnitude $1000 \mathrm{N} {\mathrm{C}}^{-1}$ is produced between two parallel plates having a separation of $2.0 \mathrm{cm}$ as shown in figure. (a) What is the  potential difference between the plates? (b) With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may reach the upper plate? (c) Suppose the electron is projected from the lower plate with the speed calculated in part (d). The direction of projection makes angle of $60°$ with the field. Find the maximum height reached by the electron.

Some equipotential surface are shown in the figure. What can you say about the magnitude and the direction of the electric field?

The electric potential existing in space is $V \left(x,y,z\right)=A \left(xy+yz+zx\right)$. (a) Write the dimensional formula of $A$. (b) Find the expression for the electric field. (c) If $A$ is $10 \mathrm{SI}$ units, find the magnitude of the electric field at $\left(1m, 1m, 1m\right)$.

An electric field $\overrightarrow{\mathrm{E}}=\left(20\hat{\mathrm{i}}+30\hat{\mathrm{j}}\right) \mathrm{N} {\mathrm{C}}^{-1}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at $\left(2 \mathrm{m}, 2 \mathrm{m}\right)$

An electric field $\overrightarrow{\mathrm{E}}=Ax\overrightarrow{\mathrm{i}}$ exists in the space, where $A=10 \mathrm{V} {\mathrm{m}}^{-2}$. Take the potential at $(10 \mathrm{m}, 20 \mathrm{m})$ to be zero. Find the potential at the origin.

The electric potential decreases uniformly from $120 \mathrm{V}$ to $80 \mathrm{V}$ as one move on the x-axis from $x=-1 \mathrm{cm}$ to $x=+1 \mathrm{cm}$. The electric field at the origin

The electric field and the electric potential at a point are $E$ and $V$, respectively.