(B) In equilibrium,the forces acting on one of the spherical balls are the tension $T$ in the thread,the electrostatic force $F_e$,and the gravitation

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(B) In equilibrium,the forces acting on one of the spherical balls are the tension $T$ in the thread,the electrostatic force $F_e$,and the gravitational force $mg$.Let the length of the thread be $L = 1\,m$ and the angle with the vertical be $\theta = 30^o$.The distance $r$ between the two charges is $r = 2L \sin(30^o) = 2 \times 1 \times 0.5 = 1\,m$.The electrostatic force is $F_e = \frac{1}{4\pi \varepsilon_0} \frac{Q^2}{r^2} = 9 \times 10^9 \times \frac{(10 \times 10^{-6})^2}{1^2} = 9 \times 10^9 \times 10^{-10} = 0.9\,N$.For equilibrium in the horizontal direction: $T \sin(30^o) = F_e$.$T \times 0.5 = 0.9$.$T = 1.8\,N$.

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

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Two small spherical balls,each carrying a charge $Q = 10\,\mu C$ ($10$ micro-coulomb),are suspended by two insulating threads of equal lengths $1\,m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $60^o$ between them,as shown in the figure. What is the tension in the threads in $N$? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,Nm^2/C^2$)

A
$18$
B
$1.8$
C
$0.18$
D
None of the above

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Electric Charges and Fields

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Electrostatic Force and Coulombs Law

Two identical conducting spheres $A$ and $B$ having charges $+q$ and $-q$ respectively are kept at a distance $d$ apart and experience a Coulombian force $F$ between them. If $50\%$ of the charge is transferred from sphere $B$ to $A$,then the new Coulombian force between them is . . . . . . .

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Two equally charged,identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. $A$ third identical,but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

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$A$ negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field of $100 \ V m^{-1}$. If the mass of the drop is $1.6 \times 10^{-3} \ g$,the number of electrons contained in the drop is:

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Five charges, each $+Q$, are placed at five vertices of a regular hexagon of side length $L$. What is the magnitude of the force on a charge $-Q$ placed at the center of the hexagon?

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Two point charges placed at a certain distance $r$ in air exert a force $F$ on each other. Then the distance $r'$ at which these charges will exert the same force in a medium of dielectric constant $k$ is given by

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Two identical conducting spheres $A$ and $B$ having charges $+q$ and $-q$ respectively are kept at a distance $d$ apart and experience a Coulombian force $F$ between them. If $50\%$ of the charge is transferred from sphere $B$ to $A$,then the new Coulombian force between them is . . . . . . .

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