S L Arora Solutions for Chapter: Electric Charges and Field, Exercise 4: HOTS Problems on Higher Order Thinking Skills

A small metal sphere carrying charge $+Q$ is located at the centre of a spherical cavity in a large uncharged metal sphere as shown in Figure. Use Gauss's theorem to find electric field at points $P_1$ and $P_2$.

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge '$Q$'. A charge '$q$' is placed at the centre of the shell.

What is the surface charge density on the inner surface of the shell?

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge '$Q$'. A charge '$q$' is placed at the centre of the shell.

What is the surface charge density on the outer surface of the shell?

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge '$Q$'. A charge '$q$' is placed at the centre of the shell.

Write the expression for the electric field at a point $x>r_2$ from the centre of the shell.

Electric field in is directed along $+X$ direction and given by $E_x =5 Ax+2B$, where $E$ is in $N{C}^{-1}$ and $x$ is in metre, $A$ and $B$ are constants with dimensions. Taking $A=10 {\mathrm{NC}}^{-1}{\mathrm{m}}^{-1}$ and $B=5 {\mathrm{NC}}^{-1}$, calculate the electric flux through the cube.

Electric field in Figure is directed along $+X$ direction and given by $E_x =5 Ax+2B$, where $E$ is in $N{C}^{-1}$ and $x$ is in metre, $A$ and $B$ are constants with dimensions. Taking $A=10 {\mathrm{NC}}^{-1}{\mathrm{m}}^{-1}$ and $B=5 {\mathrm{NC}}^{-1}$, calculate net charge enclosed within the cube.

A charge $Q$ is distributed uniformly on a ring of radius $r$. A sphere of equal radius $r$ is constructed with its centre at the periphery of the ring, Find the electric flux through the sphere.

An early model of an atom considered it to have a positively charged point nucleus of charge $Ze$, surrounded $(r>R)$ by a uniform density of negative charge up to a radius $R$. The atom as a whole is neutral. For this model, what is the electric field at a distance $r$ from the nucleus?