Two identical pendulum $A$ and $B$ are suspended from the same point. The bobs are given positive charges, with $A$ having more charge than $B$ . They diverge and reach at equilibrium, with $A$ and $B$ making angles $\theta _1$ and $\theta _2$ with the vertical respectively, Then
Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( { = {{10}^{ - 10}}m} \right)$ apart? $\left(m_{p}=1.67 \times 10^{-27} \,kg , m_{e}=9.11 \times 10^{-31}\, kg \right)$
A point charge $q_1=4 q_0$ is placed at origin. Another point charge $q_2=-q_0$ is placed at $x =12\,cm$. Charge of proton is $q_0$. The proton is placed on $x$-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is $..........cm$.
Two identical conducting spheres having unequal positive charges $q_1$ and $q_2$ separated by distance $r$. If they are made to touch each other and then separated again to the same distance, the electrostatic force between them in this case will be :-
Three charges are placed at the vertices of an equilateral triangle of side ‘$a$’ as shown in the following figure. The force experienced by the charge placed at the vertex $A$ in a direction normal to $BC$ is