Exercise-1

Three parallel metallic plates, each of area A are kept as shown in the figure and charges $Q_1, Q_2$ and $Q_3$ are given to them. Edge effects are negligible. Calculate the charges on the two outermost surfaces '$a$' and '$f$'.

Five identical plates are connected across a battery as follows :

If the charge on plate$1$ be $+q$, then the charges on the plates $2,3,4$ and $5$ are

In a certain region of space, the potential is given by $V=k\left(2x^2-y^2+z^2\right)$. The electric field at the point $\left(1,1,1\right)$ has magnitude :

Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2\mathrm{R}$ whose centre coincides with the given sphere. The flux related to imaginary sphere is:

Electric flux through a surface of area $100{ \mathrm{m}}^2$ lying in the $xy$ plane is (in $\mathrm{V}-\mathrm{m}$ ) if $E=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$:

A solid spherical conducting shell has inner radius $a$ and outer radius $2a$. At the center of the shell is located a point charge $+Q$. What must the excess charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

In the above problem, the energy density associated with the electric field will be