What is the electric field at a distance $x = \sqrt{8} R$ from the center on the axis of a charged ring with charge $Q$ and radius $R$?

Two point charges $-5 \mu C$ and $+5 \mu C$ are placed at $A$ and $B$ respectively on a straight line separated by $5 \ cm$. At a point $C$,if the resultant electric field is parallel to the line joining the points $A$ and $B$,then:

The equation of an electric field line in the $xy$-plane is given by ${x^2} + {y^2} = 1$. What is true for a particle with unit positive charge initially at rest at the point $(1, 0)$ in the $xy$-plane?

The charge distribution along the semi-circular arc is non-uniform. The charge per unit length $\lambda$ is given as $\lambda = \lambda_0 \sin \theta$,with $\theta$ measured as shown in the figure. $\lambda_0$ is a positive constant. The radius of the arc is $R$. The electric field at the center $P$ of the semi-circular arc is $E_1$. The value of $\frac{\lambda_0}{\epsilon_0 E_1 R}$ is

$A$ point charge of $10\,\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\,\mu C$ be placed so that the net electric field is zero at $x = 2\,cm$ on the $X$-axis?

The distance between a proton and an electron in a hydrogen atom is ${10^{ - 10}} \ m$. Both have a charge of magnitude $1.6 \times {10^{ - 19}} \ C$. The magnitude of the electric field intensity produced at the position of the electron due to the proton is: