The diagrams below show regions of equipotential. 
      
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) in each diagram. Choose the correct statement from the options given below:

1.	in all four cases, the work done is the same.
2.	minimum work is required to move \(q\) in figure (a).
3.	maximum work is required to move \(q\) in figure (b).
4.	maximum work is required to move \(q\) in figure (c).

A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \({S}\) is turned to position \(2,\), the percentage of its stored energy dissipated is:

       

1. \(20\%\)
2. \(75\%\)
3. \(80\%\)
4. \(0\%\)

A parallel plate air capacitor of capacitance \(C\) is connected to a cell of emf \(V\) and then disconnected from it. A dielectric slab of dielectric constant \(K,\) which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?

In a region, the potential is represented by \(V=(x,y,z)=6x-8xy-8y+6yz,\) where \(V\) is in volts and \(x,y,z\) are in meters. The electric force experienced by a charge of \(2\) coulomb situated at a point \((1,1,1)\) is:
1. \(6\sqrt{5}~\text{N}\)
2. \(30~\text{N}\)
3. \(24~\text{N}\)
4. \(4\sqrt{35}~\text{N}\)

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}\). The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\frac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

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

Three capacitors connected in series have a capacitance of \(9\) pF each. The potential difference across each capacitor if the combination is connected to a \(120\) V supply is:
1. \(10\) V
2. \(20\) V
3. \(30\) V
4. \(40\) V

Three capacitors of capacitances \(2\) pF, \(3\) pF, and \(4\) pF are connected in parallel. The charge on the \(4\) pF capacitor, if the combination is connected to a \(100\) V supply, is:
1.\(4\times10^{-10}\) C
2. \(3\times10^{-9}\) C
3. \(2\times10^{-10}\) C
4. \(1\times10^{-9}\) C

In a parallel plate capacitor with air between the plates, each plate has an area of $\mathrm{}$\(6\times10^{-3}~\text{m}^2\), and the distance between the plates is \(3~\text{mm}\). The capacitance of the capacitor is:
1. \(16.12~\text{pF}\)
2. \(17.71~\text{pF}\)
3. \(15.01~\text{pF}\)
4. \(11.32~\text{pF}\)

A \(12\) pF capacitor is connected to a \(50\) V battery. How much electrostatic energy is stored in the capacitor?
1. \(3.1\times10^{-8}\) J
2. \(2.9\times10^{-8}\) J
3. \(3.3\times10^{-8}\) J
4. \(1.5\times10^{-8}\) J