Assume that an electric field \(\vec{E}=30x^2\hat{i}\) exists in space. Then the potential difference \(V_A-V_O\), where \(V_O\) is the potential at the original and \(V_A\) the potential at \(x=2~\text{m}\) is:
1. \(-120~\text{V}\)
2. \(-80~\text{V}\)
3. \(80~\text{V}\)
4. \(120~\text{V}\)

A parallel plate capacitor is made of two circular plates separated by a distance of \(5~\text{mm}\) and with a dielectric of dielectric constant \(2.2\) between them. When the electric field in the dielectric is \(3\times 10^4~\text{V/m}\), the charge density of the positive plate will be close to:
1. \( 3 \times 10^{-7} ~\text{C} / \text{m}^2 \)
2. \( 3 \times 10^4~\text{C} / \text{m}^2 \)
3. \( 6 \times 10^4 ~\text{C} / \text{m}^2 \)
4. \( 6 \times 10^{-7}~\text{C} / \text{m}^2 \)

A uniformly charged solid sphere of radius \(R\) has potential ${\mathrm{}}_{}$\(V_0\) (measured with respect to \(\infty\)) on its surface. For this sphere, the equipotential surfaces with potentials \(\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}\) and \(\frac{V_0}{4}\) have radius \(R_1,R_2,R_3\) and \(R_4\)${\mathrm{ respectively.\; then:}}_{}$

In the given circuit, charge ${\mathrm{}}_{}$\(Q_2\) on the \(2~\mu\text{F}\) capacitor changes as \(C\) is varied from \(1~\mu\text{F}\) to \(3~\mu\text{F}\). ${\mathrm{}}_{}$\(Q_2\) as a function of '\(C\)' is given properly by: (figures are drawn schematically and are not to scale)

1.		2.
3.		4.

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge \(Q\) (having a charge equal to the sum of the charges on the \(4~\mu \text{F}\) and \(9~\mu\text{F}\) capacitors), at a point distant \(30~\text{m}\) from it, would equal:
                                       
1. \(240~\text{N/C}\)
2. \(360~\text{N/C}\)
3. \(420~\text{N/C}\)
4. \(480~\text{N/C}\)

A capacitance of \(2~\mu\text{F}\) is required in an electrical circuit across a potential difference of \(1.0~\text{kV}\). A large number of \(1~\mu\text{F}\) capacitors are available which can withstand a potential difference of not more than \(300~\text{V}\). The minimum number of capacitors required to achieve this is:
1. \(2\)
2. \(16\)
3. \(24\)
4. \(32\)