Continuous Charge Distribution

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$. A charge $q$ is placed at the centre of the shell.
What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?

A sphere has surface charge density $\sigma$. It is surrounded by a spherical shell. The surface charge density on the spherical shell is

Charge $q$ is uniformly distributed over a thin half ring of radius$R$. The electric field at the centre of the ring is

A uniformly charged conducting sphere of $2.5 \mathrm{m}$ in diameter has a surface charge density of $100 \mathrm{\mu C}\hspace{0.17em}{\mathrm{m}}^{-2}$. Calculate the
(i) Charge on the sphere. (ii) Total electric flux coming out a Gaussian surface just enclosing the outer surface of the sphere.

Total energy per unit length of a line charge in space, from perpendicular distance ${\epsilon }_0$ to $2{\epsilon }_0$, from line charge, is given by ($\lambda$ denotes charge per unit length)

A charged spherical conductor has a surface charge density of $0.7 \mathrm{C} {\mathrm{m}}^{-2}$. When its charge is increased by $0.44\mathrm{C}$, the charge density changes by $0.14 \mathrm{C} {\mathrm{m}}^{-2}$. The radius of the sphere is

Electric field at centre $O$ of semicircle of radius a having linear charge density $\lambda$ given as 

The volume charge density of a sphere of radius $R$ is represented by $\rho \left(r\right)=\beta r^2$. So, the total charge on the sphere would be _____

The charge density of a spherical distribution is given by

$\rho \left(r\right)=\left\{\begin{array}{cc}\left(\frac{{\rho }_0}{n}\right)r& r\le n\\ 0& r>n\end{array}\right.$

What is the total charge on the distribution?

A region is space contains a total positive charge $Q$ that is distributed spherically such that the volume charge density

$\rho \left(r\right)=\left\{\begin{array}{clc}\alpha & \mathrm{for} & r\le \frac{R}{2}\\ 2\alpha \left[1-\frac{r}{R}\right]& \mathrm{for} & \frac{R}{2}\le r\le R\\ 0& \mathrm{for} & r\ge R\end{array}\right.$

Where $\alpha$ is a positive constant. The value of $\alpha$ in terms of $Q$ and $R$ is

An electron moves in the field produced by a charged sphere of radius $10 \mathrm{cm}$ along the radius connecting the points separated by $12$ and $15 \mathrm{cm}$ from the centre of the sphere. The velocity of the electron changes thereby from $2\times {10}^5$ to $2\times {10}^6 \mathrm{m}/\mathrm{s}.$If the surface charge (in $nC/{\mathrm{m}}^2$ ) density of the sphere is $5.97\times x$ then find $x$ . (Mass of electron $\left.=9.1\times {10}^{-31} \mathrm{kg}\right)$

Two isolated hollow spheres of radius $2R$ and $R$ are charged to $V$ volts and $\frac{V}{2}$ volts respectively. Now the smaller sphere is inserted into the bigger sphere such that net charge on each sphere reamin same, then the potential difference between the two spheres becomes $\frac{V}{n}$. Find $n$.

Two conducting spheres of radii $r_1$ and $r_2$ have equal surface charge densities. The ratio of their charges is ___.

Describe linear charge density. Write its SI unit.

What is volume charge density? Write its SI unit.

Describe linear charge density.

What is volume charge distribution?

A rod of length $L$ has a total charge $Q$ distributed uniformly along its length. It is bent in the shape of a semicircle. Find the magnitude of the electric field at the centre of curvature of the semicircle.

Two conducting spheres of radii $r_1$ and $r_2$ have equal surface charge densities. The ratio of their charges is ___.

Explain the term volume charge density. Write its SI unit.