A polythene piece rubbed with wool is found to have a negative charge of \(3 \times10^{-7}~\text{C}\). Transfer of mass from wool to polythene is:
1. \(0.7\times10^{-18}~\text{kg}\)
2. \(1.7\times10^{-17}~\text{kg}\)
3. \(0.7\times10^{-17}~\text{kg}\)
4. \(1.7\times10^{-18}~\text{kg}\)

In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10⁵ NC^-1 per meter. What is the torque experienced by a system having a total dipole moment equal to ${10}^{-7}$ $\mathrm{C-}m$ in the negative z-direction? 

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 center of the shell. The surface charge density on the outer surfaces of the shell is:

A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:

Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then:

A particle of mass m carrying charge -q₁ is moving around a charge +q₂ along a circular path of radius r. The period of revolution of the charge -q₁ is:

1. $\sqrt{\frac{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

2. $\sqrt{\frac{8{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

3. $\sqrt{\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}}$

4. zero

Two point dipoles of dipole moment ${\overrightarrow{\mathrm{p}}}_1$ and ${\overrightarrow{\mathrm{p}}}_2$ are at a distance x from each other and ${\overrightarrow{\mathrm{p}}}_1\left|\right|{\overrightarrow{\mathrm{p}}}_2$. The force between the dipole is:

1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{4p_1{p}_2}{x^4}$

2. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{3p_1{p}_2}{x^3}$

3. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{6p_1{p}_2}{x^4}$

4. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{8p_1{p}_2}{x^4}$

A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)

If there were only one type of charge in the universe, then,

Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:

Which of the above statements are true?
1. b and d
2. a and c
3. b and c
4. c and d