A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $\mathrm{A}\left({\mathrm{m}}^2\right)$, the energy (joule) stored in the condenser is:

1. $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$

2. ${\mathrm{\epsilon }}_0\mathrm{EAd}$

3. $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2\mathrm{Ad}$

4. ${\mathrm{E}}^2\mathrm{Ad}/{\mathrm{\epsilon }}_0$

Two identical capacitors \(C_{1}\) and \(C_{2}\) of equal capacitance are connected as shown in the circuit. Terminals \(a\) and \(b\) of the key \(k\) are connected to charge capacitor \(C_{1}\) using a battery of emf \(V\) volt. Now disconnecting \(a\) and \(b\) terminals, terminals \(b\) and \(c\) are connected. Due to this, what will be the percentage loss of energy?
     
1. \(75\%\)
2. \(0\%\)
3. \(50\%\)
4. \(25\%\)

In a certain region of space with volume \(0.2\) m³, the electric potential is found to be \(5\) V throughout. The magnitude of electric field in this region is:
1. \(0.5\) N/C
2. \(1\) N/C
3. \(5\) N/C
4. zero

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: \(\left( \frac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2\right)\)
1. \(200~\text{V}\)
2. \(400~\text{V}\)
3. zero
4. \(50~\text{V}\)

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:\(\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )\)

The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:

1.		2.
3.		4.

A parallel plate capacitor with cross-sectional area \(A\) and separation \(d\) has air between the plates. An insulating slab of the same area but the thickness of \(\frac{d}{2}\) is inserted between the plates as shown in the figure having a dielectric constant, \(K=4\). The ratio of new capacitance to its original capacitance will be:

The equivalent capacitance of the combination shown in the figure is: 

Two charged spherical conductors of radii \(R_1\) and \(R_2\) are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )\) is:
1. \(\sqrt{\frac{R_1}{R_2}}\)
2. \(\frac{R^2_1}{R^2_2}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)