(B) For each sphere,three forces are acting: $(1)$ Tension force $(T)$,$(2)$ Gravitational force $(Mg)$,and $(3)$ Electrostatic repulsive force $(F)$.

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(B) For each sphere,three forces are acting: $(1)$ Tension force $(T)$,$(2)$ Gravitational force $(Mg)$,and $(3)$ Electrostatic repulsive force $(F)$.For the first sphere at equilibrium:$T_1 \cos \theta_1 = M_1 g$ and $T_1 \sin \theta_1 = F$Dividing these,we get: $\tan \theta_1 = \frac{F}{M_1 g}$For the second sphere at equilibrium:$T_2 \cos \theta_2 = M_2 g$ and $T_2 \sin \theta_2 = F$Dividing these,we get: $\tan \theta_2 = \frac{F}{M_2 g}$Since the electrostatic force $F$ between the two spheres is the same (by Newton's third law),for $\theta_1 = \theta_2$,we must have $\tan \theta_1 = \tan \theta_2$.Therefore,$\frac{F}{M_1 g} = \frac{F}{M_2 g}$,which implies $M_1 = M_2$.

Class 12 Physics Electric Charges and Fields Electrostatic Force and Coulombs Law

Difficult

Two small spheres of masses $M_1$ and $M_2$ are suspended by weightless insulating threads of lengths $L_1$ and $L_2$ respectively. The charges on the spheres are $Q_1$ and $Q_2$ respectively. The spheres are suspended such that they lie in a horizontal line and the threads make angles $\theta_1$ and $\theta_2$ with the vertical as shown in the figure. Which of the following conditions is necessary for $\theta_1 = \theta_2$?

A
$M_1 \neq M_2$ but $Q_1 = Q_2$
B
$M_1 = M_2$
C
$Q_1 = Q_2$
D
$L_1 = L_2$

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Electric Charges and Fields

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Electrostatic Force and Coulombs Law

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water,the angle remains the same. If the density of the material of the sphere is $1.5 \ g/cc$,the dielectric constant of water will be (Take density of water $= 1 \ g/cc$)

DifficultJEE MAIN 2024

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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}} = $ . . . . . . .

EasyGUJCET 2018

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Two charges of magnitude $5\, nC$ and $-2\, nC$ are placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ respectively in a region of space where there is no other external field. If the electrostatic potential energy of the system is $-0.5\,\mu J$,find the value of $x$ in $cm$.

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Three point charges of magnitude $5 \mu C$,$0.16 \mu C$,and $0.3 \mu C$ are located at the vertices $A$,$B$,and $C$ of a right-angled triangle whose sides are $AB = 3 \, cm$,$BC = 3 \sqrt{2} \, cm$,and $CA = 3 \, cm$. Point $A$ is the right-angle corner. Calculate the magnitude of the net electrostatic force (in $N$) experienced by the charge at point $A$ due to the other two charges.

MediumJEE MAIN 2022

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The force between two point charges $q_1$ and $q_2$ placed in a vacuum at a distance $r \ cm$ apart is $F$. The force between them when placed in a medium having a dielectric constant $K=5$ at a distance $r/5 \ cm$ apart will be:

DifficultJEE MAIN 2024

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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}} = $ . . . . . . .

Two charges of magnitude $5\, nC$ and $-2\, nC$ are placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ respectively in a region of space where there is no other external field. If the electrostatic potential energy of the system is $-0.5\,\mu J$,find the value of $x$ in $cm$.

The force between two point charges $q_1$ and $q_2$ placed in a vacuum at a distance $r \ cm$ apart is $F$. The force between them when placed in a medium having a dielectric constant $K=5$ at a distance $r/5 \ cm$ apart will be:

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