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:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right) \)

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:

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 \(\dfrac{d}{2}\) is inserted between the plates as shown in the figure, having a dielectric constant, \(K=4.\) The ratio of the new capacitance to its original capacitance will be:

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. \(25\%\)

Two metallic spheres of radii \(1~\text{cm}\) and \(3~\text{cm}\) are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2} ~\text{C}\), respectively. If these are connected by a conducting wire, then the final charge on the bigger sphere is:

A parallel plate capacitor has a uniform electric field \(E\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A,\) the energy stored in the capacitor is:

Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is: