Superposition Principle

Three charged particles are in equilibrium under their electrostatic forces only.

A ball at $O$ is in equilibrium as it is attached with two strings $AO$ and $DO,$ which are tied at $A$ and $D.$ $AO=DO=a\sqrt{5}$. The charges at $A,B,C$ and $D$ are $+q, +Q, +2Q$ and $-q,$ respectively. Find the correct options. The ball at $O$ is positively charged.

The figure shows two-point charges $2Q\left(>0\right)$ and $-Q$. The charges divide the line joining them into three parts $\mathrm{I}$, $\mathrm{II}$ and $\mathrm{III}$.

Consider two identical charges placed distance $2d$ apart, along the $x$-axis (see figure). The equilibrium of a positive test charge placed at point $O$ midway between them is,

In arrangement shown in figure, two positive charges, $+Q$ each are fixed. Mark the correct statement (s) regarding a third charged particle $q$ placed at the midpoint $P$ that can be displaced along or perpendicular to the line connecting the charges.

Two points charges ($Q$ each) are placed at $\left(0,y\right)$ and $\left(0,-y\right).$ A point charge $q$ of the same polarity can move along the $x$-axis. Then

Two charges $q_1$ and $q_2$ are kept on the $x$-axis and the electric field at different points on the $x$-axis is plotted against $x.$ Choose the correct statement about the nature and magnitude of $q_1$ and $q_2.$

Four charges $Q_1, Q_2, Q_3$ and $Q_4$ of same magnitude are fixed along the $x$ axis at $x=-2a, -a, +a$ and $+2a,$ respectively. $A$ positive charge $q$ is placed on the positive $y$ axis at a distance $b>0.$ Four options of the signs of these charges are given in List I. The direction of the forces on the charge $q$ is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then the $Q/q$ equals

The corners $A$, $B$, $C$ and $D$ of a square are occupied by charges $q$, $-q$, $2Q$ and $Q$, respectively. The side of the square is $2b$. The field at the midpoint of a side $CD$ is zero. What is the value of $\frac{q}{Q}$?

Given are four arrangements of three fixed electric charges. In each arrangement, a point labelled $P$ is also identified. A test charge $+q$ is placed at $P$. All the charges are of the same magnitude $Q$, but they can be either positive or negative as indicated. The charges and point $P$ all lie on a straight line. The distances between adjacent items, either between two charges or between a charge and point $P$, are all the same.

The correct order of choices in decreasing order of magnitude of the force on the $P$ is

Three positive point charges $q_1$, $q_2$ and $q_3$ from an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with the same speed maintaining angles as shown in the figure. The charge $q_1$ experiences a force $f_1$ due to the other two charges. Similarly, $q_2$ experiences a force $f_2$ and $q_3$, a force $f_3$.

Three positive point charges $q_1$, $q_2$ and $q_3$ from an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with the same speed maintaining angles as shown in the figure. The charge $q_1$ experiences a force $f_1$ due to the other two charges. Similarly, $q_2$ experiences a force $f_2$ and $q_3$, a force $f_3$. The ratio $f_1:f_2:f_3$ is

A point charge $+Q$ is placed at the centroid of an equilateral triangle. When a second charge $+Q$ is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge is $8 \mathrm{N}$. The magnitude of the net force on the central charge when a third charge $+Q$ is placed at another vertex of the triangle is

Three charges (each $Q$) are placed at the three corners of an equilateral triangle. A fourth charge $q$ is placed at the centre of the triangle. The ratio $\left|\frac{q}{Q}\right|$ so as to make the system in equilibrium is

Four point charges are placed at the corners of a square with diagonal $2a$ as shown. What is the total electric field at the center of the square?

Four identical charges $Q$ are fixed at the four corners of a square of side $a$. The electric field at a point $P$ located symmetrically at a distance $\frac{\mathit{a}}{\sqrt{\mathit{2}}}$ from the centre of the square is

It is required to hold equal charges $q$ in equilibrium at the corners of a square. What charge when placed at the centre of the square will do this?

Five point charges, each of value $+q$, are placed on five vertices of a regular hexagon of side $L$. The magnitude of the force on a point charge of value $-q$ coulomb placed at the center of the hexagon is

Three positive charges of equal magnitude $q$ are placed at the vertices of an equilateral triangle of side $\mathrm{l}$. How can the system of charges be placed in equilibrium?