In a Van-de-Graff type generator, a spherical metal shell is to be a 15×${10}^6$ V electrode. The dielectric strength of the gas surrounding the electrode is $5\times {10}^7$ V/m. What is the minimum radius of the spherical shell required?

1. 20 cm
2. 30 cm
3. 25 cm
4. 35 cm

Three isolated equal charges are placed at the three corners of an equilateral triangle as shown in the figure. The statement which is true for net electric potential V and net electric field intensity E at the centre of the triangle is:

1. $\mathrm{E}=0, \mathrm{V}=0$

2. $\mathrm{V}=0, \mathrm{E}\ne 0$

3. $\mathrm{V}\ne 0, \mathrm{E}=0$

4. $\mathrm{V}\ne 0, \mathrm{E}\ne 0$

The potential at a point 0.1 m from an isolated point charge is +100 volt. The nature of the point charge is:

1. Positive

2. Negative

3. Zero

4. Either positive or zero

A charge of 10$\mathrm{\mu }$C is placed at the origin of the x-y coordinate system. The potential difference between two points (0, a) and (a, 0) in volt will be:

1. $\frac{9\times {10}^4}{\mathrm{a}}$

2. $\frac{9\times {10}^4}{\mathrm{a}\sqrt{2}}$

3. $\frac{9\times {10}^4}{2\mathrm{a}}$

4. Zero

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