Superposition Principle and 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 hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed

Which of the following has a dipole moment is zero in the absence of an electric field.

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

Three charges each of $+1 \mathrm{\mu }\mathrm{C}$ are placed at the corners of an equilateral triangle. If the force between any two charges be $F$, then the net force on either charge will be:

Two identical positive charges are fixed at $(0, b)$ and $(0,-b).$ A particle with negative charge starts from negative $x-$axis at a large distance from $O,$ moves along the $x-$axis, passes through $O$ and moves far away from $O.$ The particle's acceleration is $a\hat{i}.$ $a$ is plotted against its $x-$coordinate. Which of the following best represents the plot?

There is a conducting shell of inner radius $8 \mathrm{cm}$ and outer radius $10 \mathrm{cm}.$ Inside this shell, there is a charge of $(+5\mu \mathrm{C})$ at a distance of $5 \mathrm{cm}$ from the centre of the shell, then the force experienced by a charge $(+10\mu \mathrm{C})$ at $a$ distance $12 \mathrm{cm}$ from the centre is $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$

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

Find the total charge on a thin disc of radius $R$, if its surface charge density varies with distance $r$ from centre as $\sigma ={\sigma }_0\frac{R}{r}$. 

What will be the potential difference between two points $\mathrm{A}$ and $\mathrm{B}$ in front of an infinitely long line of charge of linear charge density $\lambda$, as shown in figure ?

Three large identical conducting sheets, each having a surface area of $A$ is placed parallel to each other at finite distance contain charges $Q, -2Q$ and $3Q$. What is the magnitude of electric field at point$P$? 

Cotyledons are also called-

Two metal spheres, one of radius $R$ and the other of radius $2R$ , both have same surface charge density $\sigma$ . If they are brought in contact and separated, then the new surface charge density on each of the sphere are respectively

Which of the following figures correctly shows the top view sketch of the electric field lines for a uniformly charged hollow cylinder as shown in figure?

A unit negative charge with mass $M$ resides at the mid-point of the straight line of length $2a$ adjoining two fixed charges of magnitude $+Q$ each. If it is given a very small displacement $x\left(x<<a\right)$ in a direction perpendicular to the straight line, it will

Three identical charges are placed on three vertices of a square. If the force acting between $q_1$ and $q_2$ is $F_{12}$ and between $q_1$ and $q_3$ is $F_{13}$ then $\frac{F_{13}}{F_{12}}= \_\_\_\_\_\_\_\_.$

Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the infinite line of charge with linear charge density is passing through its centre and perpendicular to the plane of rod.

A charge $q_1$ exerts some force on a second charge $q_2$ . If third charge $q_3$ is brought near, the force of $q_1$ exerted on $q_2$

A small element $l$ is cut from a circular ring of radius $\alpha and \lambda$ charge per unit length. The net electric field at the centre of ring is

Two infinitely long line charge of same linear charge density $\mathrm{\lambda }$ are arranged as shown in figure. The magnitude of electric field intensity at point $P$ as shown in figure -