Four charges of the same magnitude q are placed at four corners of a square of side a. The value of the electric potential at the centre of the square will be: (Where $\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$)

1. $\frac{4\mathrm{kq}}{\mathrm{a}}$

2. $4\sqrt{2}\frac{\mathrm{kq}}{\mathrm{a}}$

3. $\frac{4\mathrm{kq}}{\sqrt{2}\mathrm{a}}$

4. $\frac{\mathrm{kq}}{\mathrm{a}\sqrt{2}}$

Two identical positive charges are placed on the y-axis at y=-a and y=+a. The variation of V (the electric potential) along the x-axis is shown by the graph:

1. 

2. 

3. 

4. 

Which graph best represents the variation of electric potential as a function of distance from the centre of a uniformly charged solid sphere of radius R?

1. 

2. 

3. 

4. 

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is:

1. Positive

2. Zero

3. Negative

4. None of these

The electric potential at a distance of 3 m on the axis of a short dipole of dipole moment $4\times {10}^{-12}$ coulomb-metre is:

1. $1.33\times {10}^{-3} \mathrm{V}$

2. 4 mV

3. 12 mV

4. 27 mV

The electric potential in volts due to an electric dipole moment of $2\times {10}^{-8}$ coulomb-metre at a distance of 3m on a line making an angle of $60°$with the axis of the dipole is:

1. Zero

2. 10 V

3. 20 V

4. 40 V

An electric dipole of length 2 cm is placed with its axis making an angle of $30°$ to a uniform electric field ${10}^5 \mathrm{N}/\mathrm{C}$. If it experiences a torque of $10\sqrt{3} \mathrm{Nm}$, then the potential energy of the dipole:

1. -10 J

2. -20 J

3. -30 J

4. -40 J

A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is:

1. $\frac{\mathrm{V}}{3\mathrm{r}}$

2. $\frac{\mathrm{V}}{4\mathrm{r}}$

3. $\frac{\mathrm{V}}{6\mathrm{r}}$

4. $\frac{\mathrm{V}}{2\mathrm{r}}$

Two concentric hollow conducting spheres of radius r and R are shown. The charge on the outer shell is Q. What charge should be given to the inner sphere so that the potential at any point P outside the outer sphere is zero?

1. $-\frac{\mathrm{Qr}}{\mathrm{R}}$

2. $-\frac{\mathrm{QR}}{\mathrm{r}}$

3. $-\mathrm{Q}$

4. $-\frac{2\mathrm{QR}}{\mathrm{r}}$

The potential gradient is a:
1. vector quantity.
2. scalar quantity.
3. conversion factor.
4. constant.