An electric field \(\vec{E} = 10 x \hat{i}\) exists in a certain region of space. Then the potential difference \(V = V_0-V_A,\) where \(V_0\) is the potential at the origin and \(V_A\) is the potential at \(x=2\) m is:

1.	\(10\) V	2.	\(-20\) V
3.	\(+20\) V	4.	\(-10\) V

What is the area of the plates of a \(2~\text{F}\) parallel plate capacitor, given that the separation between the plates is \(0.5~\text{cm}\)?
1. \(1100~\text{km}^2\)
2. \(1130~\text{km}^2\)
3. \(1110~\text{km}^2\)
4. \(1105~\text{km}^2\)

The increasing order of the electrostatic potential energies for the given system of charges is given by:

If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10~\text {volts}\) to another point where the potential is \(\text{V volts}\), then the value of \(\mathrm{V}\) is:
1. \(5~\text {volts}\)
2. \(-15~\text {volts}\)
3. \(+15~\text {volts}\)
4. \(+10~\text {volts}\)

The capacitance of a parallel plate capacitor with air as a medium is \(6~\mu\text{F}.\) With the introduction of a dielectric medium, the capacitance becomes \(30~\mu\text{F}.\)$$ The permittivity of the medium is:
\(\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )\)
1. \(1.77 \times 10^{-12}~ \text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
2. \(0.44 \times 10^{-10} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
3. \(5.00 ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
4. \(0.44 \times 10^{-13} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\)

A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}.\) The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right)\)
1. \(200~\text{V}\)
2. \(400~\text{V}\)
3. zero
4. \(50~\text{V}\)

In a certain region of space with volume \(0.2~\text m^3,\) the electric potential is found to be \(5~\text V\) throughout. The magnitude of the electric field in this region is:
1. \(0.5~\text {N/C}\) 
2. \(1~\text {N/C}\) 
3. \(5~\text {N/C}\) 
4. zero

A parallel plate air capacitor is charged to potential difference \(V\). After disconnecting the battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:

Two condensers of capacity \(0.3~\mu\text{F}\) and \(0.6~\mu\text{F}\) are connected in series. The combination is connected across a potential of \(6\) V. The ratio of energies stored by the condensers will be:
1. \(\frac{1}{2}\)
2. \(2\)
3. \(\frac{1}{4}\)
4. \(4\)