Electrostatics of Conductors

A point charge $q$ is kept inside a conducting shell of radius $2 R$ at a distance of $R$ from center. Magnitude of field due to induced charges on the inner surface of the shell at point $P$ is

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Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

A hollow uncharged spherical conductor has inner radius $a$ and outer radius $b$. A positive point charge $+q$ is in the cavity at the centre of the sphere. Find the potential $V\left(r\right)$ everywhere, assuming that $V=0$ at $r\to \infty$,

There is a conductor with cavity of radius $R$ as shown in figure. A point charge $Q$ is placed at $\frac{R}{2}$ distance from centre of cavity. A point $P$ is at $r$ distance from centre of conductor. If the electric field at point $P$ is $\frac{nQ}{\pi {\epsilon }_0{r}^2},$ then find $n.$

A particle of charge '$\mathrm{q}$' is moved from infinity to the centre of a hollow conducting spherical shell of radius $R$, thickness $t<<R$ through a very tiny hole in the shell. How much work is done by an external agent in the process?

List the applications of electrostatic shielding.

The electrostatic field inside the conductor is normal to the surface and maximum.

How will be the electrostatic field behave inside a conductor and on its surface?

Inside a conductor, there is no electric field. 

When will a device be a conductor? Write its properties.

Two long concentric hollow metallic cylinders of radii$a$and$b$, respectively carry equal and opposite charges $-\sigma$ and $+\sigma$ per unit length, as shown. The space between the cylinders is filled with air. The distance measured from the central axis is denoted by $r.$

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Which of the following statements is NOT CORRECT?

A point charge $Q$ is placed at the centre of a spherical conducting shell, the shaded part of the figure. A total charge of $-q$ is placed on the shell. The magnitude of the electric field at point $P_1$ at a distance $R_1$ from the centre and the magnitude of the electric field at point $P_2$ a distance $R_2$ from the centre are respectively

Can electric field at some point be zero though electric potential is not zero? Give example.

You are travelling in a car, lighting is expected, what should you do about your safety?

The excess charge given to a conductor reside always on its outer surface? Why?

A charge $Q$ is a given to a conducting sphere of diameter $d$. What is the value of electric field inside the sphere?

A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.

Pick up the correct statement.

Which of the following statements is "WRONG' for the conductors?

$$\begin{gathered} \mathrm{A} \mathrm{charged} \mathrm{spherical} \mathrm{conductor} \mathrm{of} \mathrm{radius} \mathit{\text{'}}R\text{'} \mathrm{is} \mathrm{connected} \mathrm{momentarily} \\ \mathrm{to} \mathrm{another} \mathrm{uncharged} \mathrm{spherical} \mathrm{conductor} \mathrm{of} \mathrm{radius} \text{'}r\mathit{ }\text{'} \mathrm{by} \mathrm{means} \mathrm{of} \mathrm{a} \\ \mathrm{thin} \mathrm{conducting} \mathrm{wire}, \mathrm{then} \mathrm{the} \mathrm{ratio} \mathrm{of} \mathrm{the} \mathrm{surface} \mathrm{charge} \mathrm{density} \mathrm{of} \\ \mathrm{the} \mathrm{first} \mathrm{to} \mathrm{the} \mathrm{second} \mathrm{conductor} \mathrm{is} \end{gathered}$$

If a wire is used to link a large metallic sphere to a smaller spherical outside and charge is given to this setup, determine whose surface density of charge will be higher.