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

In which of the following figures, the direction of electric field at point $P$ is different from others? $(\lambda$ and $-\lambda$ represent constant linear charge densities)

A circular ring carries a charge $Q$, the variation of electric field with distance $x$ measured from centre along axis for $x<<R$ is given by $E=\frac{kQx}{R^3}$ $[R\to$ Radius of Ring]. The maximum electric field on the axis will be [where $C=\frac{Q}{4\mathrm{\pi }{\epsilon }_0{R}^2}$ ]

Two non-conducting infinitely long straight wires with uniform linear charge densities ${\lambda }_1$ and ${\lambda }_2$ are arranged along $X$ and $Y$-axis respectively. Their point of intersection is at origin. One of the field lines due to these wires in $X-Y$ plane is a straight line passing through the origin. The angle made by this line with $X$-axis is

There is a non-conducting rod of length $L$ and negligible mass with two small balls each of mass $m$ and electric charge $Q$ attached to its ends. The rod can rotate in the horizontal plane about a fixed vertical axis crossing it a distance $\frac{L}{4}$ from one of its ends. A uniform horizontal electric field $E$ (along $+x$ axis) is established. At first the rod is in unstable equilibrium. In what position, the rod must be set so that if displaced a little from that position, it begins simple harmonic oscillations about the axis? 

There is a non-conducting rod of length $L$ and negligible mass with two small balls each of mass $m$ and electric charge $Q$ attached to its ends. The rod can rotate in the horizontal plane about a fixed vertical axis crossing it a distance $\frac{L}{4}$ from one of its ends. A uniform horizontal electric field $E$ (along $+x$ axis) is established. At first the rod is in unstable equilibrium. If it is disturbed slightly from this position, what would be the angular frequency of SHM in the above question?

The capacitance of a parallel plate capacitor when a very thin metallic sheet is placed in the space between the plates, parallel to the plates, will

A thin metallic strip is introduced between the plates of a parallel plate capacitor, touching the plates. How will capacitance change?

Two identical capacitors $1$ and $2$ are connected in series. The capacitor $2$ contains a dielectric slab of constant $K$ as shown. They are connected to a battery of emf $V_0$ volts. The dielectric slab is then removed. Let $Q_1$ and $Q_2$ be the charge stored in the capacitors before removing the slab and $Q{\text{'}}_1,$ and $Q{\text{'}}_2$ be the values after removing the slab. Then