B M Sharma Solutions for Chapter: Coulomb's Laws and Electric Field, Exercise 3: DPP

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

Three charges$-q_1,+q_2$ and $-q_3$ are placed as shown in the figure. The $x-$component of the force on $-q_1$ is proportional to

Two similar balloons filled with helium gas are tied to strings each of length $L.$ A body of mass $m$is tied to another end of the strings. The balloons float on air at distance $r.$ If the amount of charge on the balloons is same then the magnitude of charge on each balloon will be

Two small spheres with mass $m_1$ and $m_2$ hang from massless insulating threads of length $l_1$ and $l_2.$ The two spheres carry charges $q_1$ and $q_2$, respectively. The spheres are hung such that they are on the same horizontal level and the threads are inclined to the vertical at angles ${\theta }_1$ and ${\theta }_2.$ Which of the condition is required if ${\theta }_1={\theta }_2?$

Two identical small balls each have a mass $m$and charge $q.$ When placed in a hemispherical bowl of radius $R$with frictionless, nonconductive walls, the beads move, and at equilibrium the line joining the balls is horizontal and the distance between them is $R$(see figure). Neglect any induced charge on the hemispherical bowl. Then the charge on each bead is

$\left(\text{ here k}=\frac{1}{4\pi {\epsilon }_0}\right)$

Three similar charges $+q$are placed on $3$corners of an equilateral triangle $ABC$of side $a.$ How many minimum charges should be placed on a circle of radius $a$with the center at $A$, so that resultant force on the charge placed at the center is $\frac{q^2}{4\pi {\epsilon }_0{a}^2}$along the $x-$axis?

Four similar charges $(+q)$ are placed at the origin$O, B, C$ and $D$ as shown. The angles are as shown. Charges at $B, C$ and $D$ are equidistant from $O$ at a distance of $a.$ The forces of repulsion experienced by charge at $O$ due to charges at $B and D$ along $CO$ are equal, given by $\frac{q^2\sqrt{3}}{8\pi {\epsilon }_0{a}^2}.$ Find the relation between ${\theta }_1, {\theta }_2$ and ${\theta }_3$.

In the configuration, as shown, the $+q$charge is placed at the origin and charge $Q$and $Q^{\text{'}}$are placed at distances $a$and $a_0$respectively, from the origin. If the net electrostatic force on the charge $(+q)$ is along negative $y-$axis and ${\theta }_1={\theta }_2/2=30°,$ then $\left(Q^{\text{'}}/Q\right)$ is equal to