Embibe Experts Solutions for Chapter: Electrostatics, Exercise 1: Exercise#1

A large sheet carries uniform surface charge density $\sigma .$ A rod of length $2\ell$, has a linear charge density $\lambda$, on one half and $-\lambda$, on the second half. The rod is hinged at mid-point $O$, and makes angle $\theta$, with the normal to the sheet. The electric force experienced by the rod is

The figure shows two large, closely placed, parallel, nonconducting sheets with identical (positive) uniform surface charge densities, and a sphere with a uniform (positive) volume charge density. Four points marked as $1, 2, 3$ and $4$ are shown in the space in between. If $E_1, E_2, E_3$ and $E_4$ are the magnitude of net electric fields at these points respectively then:

Two similar very small conducting spheres having charges $40 \mu \mathrm{C}$ and $-20 \mu \mathrm{C}$ are some distance apart. Now they are touched and kept at the same distance. The ratio of the initial to the final force between them is:

The magnitude of the electric force on $2 \mu \mathrm{C}$ charge placed at the center $O$ of two equilateral triangles each of side $10 \mathrm{cm},$ as shown in the figure is $P.$ If charge $A, B, C, D, E$ and $F$ are $2 \mu \mathrm{C}, 2 \mu \mathrm{C}, 2 \mu \mathrm{C}, -2 \mu \mathrm{C}, -2 \mu \mathrm{C}, -2 \mu \mathrm{C}$, respectively, then the value of $P$ is:

There is a uniform electric field in $X$-direction. If the work done by external agent in moving a charge of $0.2 \mathrm{C}$ through a distance of $2$ $\mathrm{m}$ slowly along the line making an angle of $60°$ with $X$-direction is $4$ $\mathrm{J}$, then the magnitude of $E$ is:

Two equal positive charges are kept at points $A$ and $B.$ The electric potential, while moving from $A$ to $B$ along straight line:

A semicircular ring of radius $0.5 \mathrm{m}$ is uniformly charged with a total charge of $1.5\times {10}^{-9}$ $\mathrm{C}$. The electric potential at the center of this ring is:

A $5$ $\mathrm{C}$ charge experiences a constant force of $2000 \mathrm{N}$, when moved between two points separated by a distance of $2 \mathrm{cm}$ in a uniform electric field. The potential difference between these two points is: