Electrostatics

A particle of mass $m_1$ and electric charge $q$ starts from rest under the influence of a uniform external electric field $\mathbf{E}$ to travel a distance $d$ in time $t_1$. If the particle had mass $m_2$, it would take time $t_2$ to trav...

Three infinite plane sheets which have uniform positive surface charge densities $\sigma$, $\sigma$ and $2\sigma$, are arranged parallel to each other with a separation of $d$ as shown in the figure. A spherical Gaussian surface $S$ of radi...

A particle of charge $q=1 e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates of length $l$ as illustrated in the figure. The potential difference between the two plates is 1 V and their separation...

Consider two point charges $+q$ and $+2 q$ fixed on the $x-y$ plane at $(-\ell / 2,0)$ and $(+\ell / 2,0)$ respectively. Another point charge $-q$ having mass $m$ is released from rest at $(0,(\sqrt{3} / 2) \ell)$ on the $x y$ plane, as sho...

Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the follow...

Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measur...

A conducting sphere of radius $a$ initially contains a uniform volume charge density $\rho$. What is the electric flux $\Phi$ through a spherical surface of radius $2 a$ centered at a point on the surface of the charged sphere (see figure) ...

Two uniformly charged concentric thin spherical shells of radii $r_1$ and $r_2$ have charges $+Q$ and $-Q$, respectively. How does the electrostatic potential vary with distance from the center of the shells?

The charge distribution inside a sphere of radius $R=2 a / b$ is given by the volume charge density $\rho=a r^2-b r^3$, where $a$ and $b$ are constants and $r$ is the radial distance from the center of the sphere. At what distance from the...