Embibe Experts Solutions for Chapter: Electrostatics, Exercise 1: KEAM 2020

A point charge $+ Q$ is held at rest at a point $P.$ Another point charge $-q$ , whose mass is $m$ , moves at a constant speed $v$ in a circular orbit of radius $R_1$ around $P$. The work required to increase the radius of revolution of $-q$ from $R_1$, to another orbit $R_2$ is $\left(R_2>R_1\right)$ $\left(\text{where\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}K=\frac{1}{4\pi {\epsilon }_0}\right)$

The distance between two charges $q_1=+2\mu C$ and $q_2=+8\mu C$ is $15 \mathrm{cm}.$ Calculate the distance from the charge $q_1$ to the points on the line segment joining the two charges where the electric field is zero.

An electron, placed in an electric field, experiences a force $F$ of $1 \mathrm{N}.$ What are the magnitude and direction of the electric field $E$ at the point where the electron is located $\left(e=1.6\times {10}^{-19} \mathrm{C}\right) ?$

The electric potential $\mathrm{V}$ at any point $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ in space is given by $\mathrm{V}=4{\mathrm{z}}^2$ volt, where $\mathrm{x},\mathrm{y},\mathrm{z}$ are all in metre. The electric field at that point $(1\mathrm{m},0,2\mathrm{m})$ in ${\mathrm{Vm}}^{-1}$ is

Four point charge (with equal magnitude of charge of $5 C;$ but with different signs) are placed at four corners of a square of side $10 \mathrm{m}.$ Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note $\left.k=\frac{1}{4\pi {\epsilon }_0}\right]$

The work done in moving a point charge of $10\mathrm{\mu C}$ through a distance of $3\mathrm{cm}$ along the equatorial axis of an electric dipole is

A point dipole with dipole moment, $p=p_0\hat{\mathrm{K}},$ is kept at the origin. An external electric field given by $E=E_0\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right),$ is applied on it. Which one of the following statement is true ?

The electric flux (in $\mathrm{SI}$ units) through any face of a cube due to a positive charge $\mathrm{Q}$ situated at the centre of a cube is