An electron is rotating around an infinite positive linear charge in a circle of radius $0.1 \,m$. If the linear charge density is $1 \,\mu C/m$,then the velocity of the electron in $m/s$ will be ...... $\times 10^7$.

As shown in the following figure,an electron falls through a distance of $1.5 \ cm$ in a uniform electric field of magnitude $2.0 \times 10^4 \ NC^{-1}$. Find the acceleration of the electron due to the electric field.

An electron of mass $m_e$ and a proton of mass $m_p$ are kept in a uniform electric field. The ratio of the acceleration of electron $(a_e)$ to the acceleration of proton $(a_p)$ is

$A$ uniform electric field of $10^3 \, V/m$ is directed along the $y$-axis. $A$ particle of mass $1 \, g$ and charge $10^{-6} \, C$ is projected from the origin into the field with a velocity of $10 \, m/s$ along the positive $x$-axis. Its speed after $10 \, s$ is (in $m/s$):

$A$ particle of charge $1\ \mu C$ and mass $1\ g$ moving with a velocity of $4\ m/s$ is subjected to a uniform electric field of magnitude $300\ V/m$ for $10\ s$. Then its final speed cannot be.......$m/s$.

Charge $Q$ is given a displacement $\vec{r} = a\hat{i} + b\hat{j}$ in an electric field $\vec{E} = E_1\hat{i} + E_2\hat{j}$. The work done is