Principle of Superposition

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

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:

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$P$? 

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 charge $Q_1=+11{\left(\frac{11}{3}\right)}^{\frac{3}{2}}\times 10^{-9} \mathrm{C}$ is located at the origin in free space and another charge $Q$ at $(2, 0, 0)$. If the $x$-component of the electric field at $(3, 1, 1)$ is zero, then the magnitudes of $Q$ in $\mathrm{nC}$ is

A uniform surface charge density $8 \mathrm{\sigma }$ exists over the entire $x-y$ plane except for a circular hole of radius a centred at the origin. The electric field at a point $P\left(0\text{, }0\text{, }\sqrt{3}a\right)$ on the $z$-axis is found to be

In a regular polygon of $\mathrm{n}$ sides, each corner is at a distance $\mathrm{l}$ from centre. Identical charges of magnitude $\mathrm{q}$ are placed at $\left(\mathrm{n}-1\right)$ corners. The field at the centre is

A regular polygon has $20$ sides. Equal charges, each $\mathrm{Q}$ , are placed at $19$ vertices of the polygon and a charge $\mathrm{q}$ is placed at the centre of the polygon. If the distance of each vertex from the centre is $\mathrm{a}$, net force experienced by $\mathrm{q}$ is

In the basic $\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{l}$ crystal structure, ${\mathrm{C}\mathrm{s}}^{+}$ and ${\mathrm{C}\mathrm{l}}^{-}$ ions are arranged in a BCC configuration as shown in Fig. The net electrostatic force exerted by the eight ${\mathrm{C}\mathrm{s}}^{+}$ ions on the ${\mathrm{C}\mathrm{l}}^{-}$ ion is

Four equal charges, each $+q$ are placed at the four corners of a square of side $a$ . Then the Coulomb force experienced by one charge due to the rest of three is

If two like charges of magnitude $1\mathrm{ }\times \mathrm{ }{10}^{-9} \mathrm{C}$  and  $9\mathrm{ }\times \mathrm{ }{10}^{-9} \mathrm{C}$  are separated by a distance of $1 \mathrm{metre}$, then the point on the line joining the charges, where the force experienced by a charge placed at that point is zero, is

Vertices of a regular hexagon, of sides $3\mathrm{ }\mathrm{c}\mathrm{m}$, have three positive and three negative charges, each of magnitude $q=1.5\mathrm{ }\mathrm{n}\mathrm{C}$, as shown in the diagram. A point charge of $Q=5 \mathrm{n}\mathrm{C}$ is placed at the centre of the hexagon. The net force on $5\mathrm{ }\mathrm{n}\mathrm{C}$ is

Vertices of a regular hexagon of sides $3\mathrm{ }\mathrm{c}\mathrm{m}$ have three positive and negative charges each of magnitude $\mathrm{\theta }=1.5\mathrm{ }\mathrm{n}\mathrm{C}$ as shown in diagram. A point charge of $Q=5 \mathrm{n}\mathrm{C}$ is placed at centre of hexagon. The net force on $5\mathrm{ }\mathrm{n}\mathrm{C}$ is -

Three charges are placed at the vertices of an equilateral triangle of sides $a$. The force experienced by the charge placed at the vertex $A$ in a direction normal to $BC$ is

The charge $Q$ is placed at each of the two opposite corners of a square and a charge $q$ is placed at each of the other two opposite corners. If charges $q$ are fixed, then for equilibrium of $Q$, it is required that-

Two identical balls each having a density $1.6\mathrm{ }\mathrm{g} \mathrm{c}{\mathrm{m}}^{-3}$ are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium, each string makes an angle $30°$ with the vertical. Now, both the balls are immersed in a liquid of density $0.8\mathrm{ }\mathrm{g} \mathrm{c}{\mathrm{m}}^{-3}$, but the angle does not change. The dielectric constant of the liquid is -

If two like charges of magnitude $1\times {10}^{-9}$ coulomb and $9\times {10}^{-9}$ coulomb are separated by a distance of $1\mathrm{ }\mathrm{m}\mathrm{e}\mathrm{tre}$, then the point on the line joining the charges, where the force experienced by a charge placed at that point is zero, is

Charges $+2\mathrm{q},\mathrm{ }+\mathrm{q}$ and $+\mathrm{q}$ are placed at the corners $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ of an equilateral triangle $\mathrm{A}\mathrm{B}\mathrm{C}$. If $E$ is the electric field at the circumcentre $\mathrm{O}$ of the triangle, due to the charge $+\mathrm{q}$, then the magnitude and direction of the resultant electric field at $\mathrm{O}$ is:

Four charges, each having charge $+\mathrm{q}$, are located at the vertices of square $\mathrm{ABCD}$ of side $a$ as shown in the figure. Find the electric field $E$ at the mid-point of side $\mathrm{BC}$.

Find the net force on $-2\text{q}$.