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:

        

1.	\(\frac{3qQ}{4\pi \varepsilon_0 a}\)	2.	\(\frac{3qQ}{8\pi \varepsilon_0 a}\)
3.	\(\frac{qQ}{4\pi \varepsilon_0 a}\)	4.	\(\text{zero}\)

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:

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. \(10~\mu\text{F}\)

Eight equally charged tiny drops are combined to form a big drop. If the potential on each drop is 10 V, then the potential of the big drop will be:

A bullet of mass 2 g is having a charge of 2 µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?
1. 50 kV
2. 5 V
3. 50 V
4. 5 kV 
 

A capacitor of capacity C₁ is charged up to V volt and then connected to an uncharged capacitor C₂. Then final P.D. across each will be:

1. $\frac{{\mathrm{C}}_2\mathrm{V}}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

2. $\frac{{\mathrm{C}}_1\mathrm{V}}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

3. $\left(1+\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1}\right)$

4. $(1-\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1})\mathrm{V}$

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.

Consider a uniform electric field in the Z-direction. The potential is constant:

1.  (a, b, c)
2.  (a, c, d)
3.  (b, c, d)
4.  (c, d)

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d₁ and dielectric constant K₁ and the other has thickness d₂ and dielectric constant K₂, as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness d = d₁ + d₂ and effective dielectric constant K. K is:  

In a region of constant potential:

Choose the correct statement(s): 
1. b and c
2. a and c
3. b and d
4. c and d