Four charges $+Q,-Q,+Q,-Q$ are placed at the corners of a square taken in order. At the centre of the square 

1. $E=0,V=0$

2. $E=0,V\ne 0$

3. $E\ne 0,V=0$

4. $E=0,V\ne 0$

Point charge q₁ = 2 μC and q₂ = –1 μC are kept at points x = 0 and x = 6 respectively. Electrical potential will be zero at points 

1. x = 2 and x = 9

2. x = 1 and x = 5

3.  x = 4 and x = 12

4. x = –2 and x = 2

Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction are 

1. Planes parallel to yz-plane

2. Planes parallel to xy-plane

3. Planes parallel to xz-plane

4. Coaxial cylinders of increasing radii around the x-axis

A bullet of mass 2 gm 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. 5 kV

2. 50 kV

3.  5 V

4. 50 V

In a certain charge distribution, all points having zero potential can be joined by a circle $S.$ The points inside $S$ have positive potential, and points outside $S$ have a negative potential. A positive charge, which is free to move, is placed inside $S.$ What is the correct statement about $S$:

A square of side ‘a’ has charge Q at its centre and charge ‘q’ at one of the corners. The work required to be done in moving the charge ‘q’ from the corner to the diagonally opposite corner is -

1. Zero

2. $\frac{Qq}{4\pi {\in }_{0}a}$

3. $\frac{Qq\sqrt{2}}{4\pi {\in }_{0}a}$

4. $\frac{Qq}{2\pi {\in }_{0}a}$

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is

1. Zero

2. $\left(\frac{{\displaystyle -qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\sqrt{2}a$

3. $\left(\frac{{\displaystyle qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\frac{a}{\sqrt{2}}$

4. $\left(\frac{{\displaystyle qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\sqrt{2}a$

Two charges $q_1$ and $q_2$ are placed $30~\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40~\text{cm}$ from $C$ to $D.$ The change in the potential energy of the system is $\dfrac{q_{3}}{4 \pi \varepsilon_{0}} k,$ where $k$ is:

Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is -

1. Zero

2. $\frac{Q}{4\pi {\epsilon }_0}\left[\frac{{\displaystyle 1}}{{\displaystyle R}}-\frac{{\displaystyle 1}}{{\displaystyle \sqrt{R^2+d^2}}}\right]$

3. $QR/4\pi {\epsilon }_0{d}^2$

4. $\frac{Q}{2\pi {\epsilon }_0}\left[\frac{{\displaystyle 1}}{{\displaystyle R}}-\frac{{\displaystyle 1}}{{\displaystyle \sqrt{R^2+d^2}}}\right]$