The dipole moment of a water molecule is $6.3\times {10}^{-30}\mathrm{Cm}$. A sample of water contains ${10}^{21}$ molecules, whose dipole moments are all oriented in an electric field of strength $2.5\times {10}^5\mathrm{N}/\mathrm{C}$. Calculate the work to be done to rotate the dipoles from their initial orientation ${\mathrm{\theta }}_1=0$ to one in which all the dipoles are perpendicular to the field, ${\mathrm{\theta }}_2={90}^{\circ }$

A charge $6 \mathrm{\mu C}$ is placed at the origin and another charge $-5\mathrm{\mu C}$  is placed on the y axis at a position $\mathrm{A} (0,6.0) \mathrm{m}$. 

Calculate the total electric potential at the point P whose coordinates are $(8.0,0) \mathrm{m}$ 

A charge $6 \mathrm{\mu C}$ is placed at the origin and another charge $-5\mathrm{\mu C}$  is placed on the y axis at a position $\mathrm{A} (0,6.0) \mathrm{m}$. 

Calculate the work done to bring a proton from infinity to the point $P$. What is the significance of the sign of the work done ?  

In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3}{\mathrm{m}}^2$ and the separation between the plates is $2 \mathrm{mm}$.

Calculate the capacitance of the capacitor,

In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3}{\mathrm{m}}^2$ and the separation between the plates is $2 \mathrm{mm}$.

If this capacitor is connected to $100 \mathrm{V}$ supply, what would be the charge on each plate?

In a parallel plate capacitor with air between the plates, each plate has an area of $6\times {10}^{-3}{\mathrm{m}}^2$ and the separation between the plates is $2 \mathrm{mm}$.

How would charge on the plates be affected if a $2 \mathrm{mm}$ thick mica sheet of $\mathrm{k}=6$ is inserted between the plates while the voltage supply remains connected? 
 

Find the equivalent capacitance between $P$ and $Q$. Given, area of each plate $= A$ and separation between plates $= d$.