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:
1. \(\frac{E^2 Ad}{\varepsilon_0}\)
2. \(\frac{1}{2}\varepsilon_0E^2 Ad\)
3. \(\varepsilon_0EAd\)
4. \(\frac{1}{2}\varepsilon_0E^2 \)

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:

The electric potential V at any point (x, y, z), all in meters in space is given by V = $4{\mathrm{x}}^{\mathrm{2 }}$volt. The electric field at the point (1, 0, 2) in volt/meter, is:

Two parallel metal plates having charges +Q and –Q, face each other at a certain distance between them. If the plates are now dipped in the kerosene oil tank, the electric field between the plates will:

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:
1. \(3\times 10^{-2}~ \text{C}\)
2. \(4\times 10^{-2}~\text{C}\)
3. \(1\times 10^{-2}~\text{C}\)
4. \(2\times 10^{-2}~\text{C}\)

A capacitor is charged with a battery and energy stored is U. After disconnecting the battery another capacitor of the same capacity is connected in parallel with it. The energy stored in each capacitor is:

1. U/2

2. U/4

3. 4 U

4. 2 U

Two charges q₁ and q₂ are placed 30 cm apart, as shown in the figure. A third charge q₃ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{\mathrm{q}}_3}{4\mathrm{\pi }{\in }_0}\mathrm{k}$ , where k is:

.

1. 8q₂

2. 6q₂

3. 8q₁

4. 6q₁

As per this diagram, a point charge \(\mathrm{+q}\) is placed at the origin \(\mathrm{O}.\) Work done in taking another point charge \(\mathrm{-Q}\) from the point \(\mathrm{A},\) coordinates \((\mathrm{0,a}),\) to another point \(\mathrm{B},\) coordinates \((\mathrm{a,0}),\) along the straight path \(\mathrm{AB}\) is:

A network of four capacitors of capacity equal to ${\mathrm{C}}_1=\mathrm{C},{\mathrm{ C}}_2=2\mathrm{C},{\mathrm{ C}}_3=3\mathrm{C}\text{, and }{\mathrm{C}}_4=4\mathrm{C}$ is conducted to a battery as shown in the figure. The ratio of the charges on ${\mathrm{C}}_2\text{ and }{\mathrm{C}}_4$ is:

1. $\frac{7}{4}$

2. $\frac{22}{3}$

3. $\frac{3}{22}$

4. $\frac{4}{7}$

The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:

1. \(6~\mu\text{F}~\)
2. \(20~\mu\text{F} ~\)
3. \(3~\mu\text{F}~\)
4. \(10~\mu\text{F}\)