Embibe Experts Solutions for Chapter: Electrostatics, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

A point charge of $50 \mu \mathrm{C}$ is placed in the $XY$ plane at a location with radius vector ${\overrightarrow{r}}_0=2\hat{\mathrm{i}}+3\hat{\mathrm{j}} \mathrm{m}$ The electric field strength and its magnitude at a point with radius vector $\overrightarrow{r}=8\hat{\mathrm{i}}-5\hat{\mathrm{j}} \mathrm{m}$ is $\left({\epsilon }_o=8.85\times {10}^{-12} {\mathrm{C}}^2 \mathrm{N}-{\mathrm{m}}^{-2}\right)$

An infinite line of charge with uniform line charge density of $1 \mathrm{C} {\mathrm{m}}^{-1}$ is placed along the $\mathrm{y}$-axis. A charge of $1\mathrm{C}$ is placed on the $\mathrm{x}$-axis at a distance of $d=3 \mathrm{m}$ from the origin. At what distance $\left(r\right)$ from the origin on the $\mathrm{x}$-axis, the total electric field is zero.$N$ (Assume $0<r<d$)

A circular wire loop of radius, $10 \mathrm{cm}$ carries a total charge of, ${10}^{-5}\mathrm{C}$ distributed uniformly over its length. A small length of, $3.14\times {10}^{-6} \mathrm{m}$ of wire is cut off. The magnitude of the electric field at the centre due to the remaining wire is,
(Assume $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$ SI units)

Two infinitely long thin straight wires having uniform linear charge densities $2\lambda$ and $3\lambda$ are arranged parallel to each other at a distance $R$ apart. The intensity at a point midway between them is

A semi-infinite non conducting rod lies along $+x$-axis with its left end at the origin. The rod has uniform linear charge density $\lambda .$ The magnitude of electric field $\left|\overrightarrow{E}\right|$ at a point on the $y$-axis at the distance $L$ from the origin, will be

A particle of mass $m$ and charge $q$ is thrown perpendicular to an electric field of intensity $E$ with an initial velocity $v.$ The particle moves a distance $x$ perpendicular to the field and a distance $y$ along the direction of the field. If $y=\alpha x^2$ then the $\alpha$ is given by

The work done to assemble the three charges in a configuration as shown in the figure below is

Consider the charged cylindrical capacitor. The magnitude of electric field $\overrightarrow{E}$ in its annular region