B M Sharma Solutions for Chapter: Coulomb's Laws and Electric Field, Exercise 5: DPP

Two identical point charges are placed at a separation of $d$. $P$is a point on the line joining the charges, at a distance $x$from any one of the two charges. The field at $P$is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $d$. Which of the following represents the resulting curve?

The bob of a pendulum of mass $8 \mathrm{\mu g}$carries an electric charge of $39.2\times {10}^{-10}$ $\mathrm{C}$ in an electric field of $20\times {10}^3 \mathrm{V} {\mathrm{m}}^{-1}$ and it is at rest. The angle made by the pendulum with the vertical will be

Two charges each equal to $\eta q\left({\eta }^{-1}<\sqrt{3}\right)$ are placed at the corners of an equilateral triangle of side$a$. The electric field at the third corner is $E_3$ where $\left(E_0=\frac{q}{4\pi {ϵ}_0{a}^2}\right)$

Two point charges$(+Q)$ and $(-2Q)$ are fixed on the $x$-axis at positions $a$and $2a$from the origin, respectively. At what positions on the axis, the resultant electric field is zero?

A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed

An electron falls through a small distance in a uniform electric field of magnitude $2\times {10}^4 \mathrm{N} {\mathrm{C}}^{-1}$. The direction of the field is reversed keeping the magnitude unchanged and a proton falls through the same distance. The time of fall will be

There is a uniform electric field of strength ${10}^3 \mathrm{V} {\mathrm{m}}^{-1}$ along $y$-axis. A body of mass $1 \mathrm{g}$ and charge ${10}^{-6} \mathrm{C}$ is projected into the field from origin along the positive $x$-axis with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. Its speed in $\mathrm{m} {\mathrm{s}}^{-1}$ after $10 \mathrm{s}$ is (neglect gravitation)

In the figure shown, there is a large sheet of charge of uniform surface charge density $\sigma$. A charge particle of charge $-q$ and mass $m$ is projected from a point $A$ on the sheet with a speed $u$ with angle of projection such that it lands at maximum distance from $A$ on the sheet. Neglecting gravity, find the time of flight.