Exercise 1

A uniformly charged conducting sphere of $2.5 \mathrm{m}$ in diameter has a surface charge density of $100 \mathrm{\mu C}\hspace{0.17em}{\mathrm{m}}^{-2}$. Calculate the
(i) Charge on the sphere. (ii) Total electric flux coming out a Gaussian surface just enclosing the outer surface of the sphere.

A charge q is located at the centre of a cube. The electric flux through any two consecutive faces will be

Two conducting spheres of radii $3 \mathrm{cm}$ and $1 \mathrm{cm}$ are separated by a distance of $10 \mathrm{cm}$ in free space. If the spheres are charged to same potential of $10 \mathrm{V}$ each, the force of  repulsion between them is

Two identical point charges of magnitude $Q$  are kept at a distance $r$ from each other. A third point charge $q$ is placed on the line joining the above two charges, such that all the three charges are in equilibrium. What is the magnitude of the third charge?

The identical point charges, $q$ each, are kept $2 \mathrm{m}$ apart in air. A third point charge $Q$ of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of $Q$.

Which of the following represents electric field neither constant in magnitude nor in direction?

How many electrons must be removed from a body so that it may have the charge of

i. $1 \mathrm{million} \mathrm{coulombs}$

ii. $1 \mathrm{micro} \mathrm{coulomb}$

When a scale is rubbed with hair two electrons are transferred from scale to hair. Calculate the charge on hair or scale after transfer .