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 $……….cm$.

A charge $+q$ is situated at a distance $d$ away from both the sides of a grounded conducting $L$ shaped sheet as shown in the figure.The force acting on the charge $+q$ is 

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 $q_1$ exerts an electric force on a second point charge $q_2$. If third charge $q_3$ is brought near, the electric force of $q_1$ exerted on $q_2$

Two small metal balls of different masses $m_1$ and $m_2$ are connected by strings of equal length to a fixed point. When the balls are given equal charges, the angles that the two strings make with the vertical are $30^{\circ}$ and $60^{\circ}$, respectively. The ratio $m_1 / m_2$ is close to