Embibe Experts Solutions for Chapter: Electrostatics, Exercise 3: Exercise-3

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $\frac{Q}{q}$equals:

In a uniformly charged sphere of total charge $Q$ and radius $R,$ the electric field $E$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be:

A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the  end $A$ is

A long cylindrical shell carries a positive surface charge $\sigma$ in the upper half and a negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like the figure given in: (figures are schematic and not drawn to scale)

A uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3V_0}{2}, \frac{5V_0}{4}, \frac{3V_0}{4}$ and $\frac{V_0}{4}$ have radius $R_1, R_2, R_3$ and $R_4$, respectively. Then

The region between two concentric spheres of radii $\text{'}a\text{'}$ and $\text{'}b\text{'},$ respectively (see figure), has volume charge density $\rho =\frac{A}{r},$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q.$ The value of $A$ such that the electric field in the region between the spheres will be constant, is:

The given graph shown variation (with distance $r$ from centre) of:

Three charges $Q,+q$ and $+q$ are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is :