31.

If the electric flux entering and leaving a closed surface are 6 x 10⁶ and 9 x 10⁶ SI units respectively, then the charge inside the surface of permittivity of free space ε₀ is

• ε₀ × 10⁶

• − ε₀ × 10⁶

• − 2ε₀ × 10⁶

• 3ε₀ × 10⁶

Two identical thin rings, each of radius 10 cm carrying charges 10 C and 5 C are coaxially placed at a distance 10 cm apart. The work done in moving a charge q from the centre of the first ring to that of the second is

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle +}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle -}{\displaystyle 1}{\displaystyle }}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle +}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle -}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

Choose the correct statement

• Polar molecules have permanent electric dipole moment

• CO₂  molecule is a polar molecule 

• H₂O  is a non-polar molecule

• The dipole field at large distances falls of as $\frac{1}{{\mathrm{r}}^2}$

The electric field between two infinitely charged plates with air medium in between, in terms of the surface charge density σ is

• $4{\mathrm{\pi \epsilon }}_0$

• $\frac{\mathrm{\sigma }}{4{\mathrm{\pi \epsilon }}_0}$

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$

• $\frac{4\mathrm{\pi \sigma }}{{\mathrm{\epsilon }}_0}$

Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire. The total electric flux passing through the cylindrical surface is

• $\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0}$

• $\frac{100 \mathrm{Q}}{{\mathrm{\epsilon }}_0}$

• $\frac{10 \mathrm{Q}}{{\mathrm{\pi \epsilon }}_0}$

• $\frac{100 \mathrm{Q}}{{\mathrm{\pi \epsilon }}_0}$

A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q is shot with speed 2v, the closest approach would be

• $\frac{\mathrm{r}}{4}$

• $\frac{\mathrm{r}}{2}$

• 2r

• r

A dipole of electric dipole moment p is placed in a uniform electric field of strength E. If θ is the angle between positive directions of p and E, then the potential energy of the electric dipole is largest when θ is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\mathrm{\pi }$

• zero

Two conducting spheres of radii 3 cm and 1 cm are separated by a. distance of 10 cm in free space. If the spheres are charged to same potential of 10 V each, the force of repulsion between them is

• $\left(\frac{1}{3}\right) \times {10}^{-9} \mathrm{N}$

• $\left(\frac{2}{9}\right) \times {10}^{-9} \mathrm{N}$

• $\left(\frac{1}{9}\right) \times {10}^{-9} \mathrm{N}$

• $\left(\frac{4}{9}\right) \times {10}^{-9} \mathrm{N}$

If q₁ + q₂ = q, then the value of the ratio $\frac{{\mathrm{q}}_1}{\mathrm{q}}$, for which the force between q₁ and q₂ is maximum is

• 0.25

• 0.75

• 1

• 0.5

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres ${\mathrm{\sigma }}_1/{\mathrm{\sigma }}_2$ is

• R₁ / R₂

• R₂ / R₁

• $\sqrt{\left({\mathrm{R}}_1 / {\mathrm{R}}_2\right)}$

• R₁² / R₂²