A charge q is placed at the centre of the line joining two equal point charges each equal to Q. The system of 3 charges will be in equilibrium if q is equal to

• $+ \frac{\mathrm{Q}}{4}$

• $- \frac{\mathrm{Q}}{2}$

• $+ \frac{\mathrm{Q}}{2}$

• $- \frac{\mathrm{Q}}{4}$

The inward and outward electric flux from a closed surface are respectively 8 x 10³ and 4 x 10³ units. Then the net charge inside the closed surface is

• − 4 × 10³ coulomb

• 4 × 10³ coulomb

• $\frac{- 4 \times {10}^3}{{\mathrm{\epsilon }}_0} \mathrm{coulomb}$

• − 4 × 10³ ε₀ coulomb

A charged particle of mass m and charge q is released from rest in an uniform electric field E neglecting the effect of gravity, the kinetic energy of the charged particle after 't' second is

• $\frac{2{\mathrm{E}}^2{\mathrm{t}}^2}{\mathrm{mq}}$

• $\frac{{\mathrm{Eq}}^2\mathrm{m}}{2{\mathrm{t}}^2}$

• $\frac{\mathrm{Eqm}}{\mathrm{t}}$

• $\frac{{\mathrm{E}}^2{\mathrm{q}}^2{\mathrm{t}}^2}{2\mathrm{m}}$

A cylinder of radius r and length l is placed in an uniform electric field E parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by

• zero

• 2πr²E

• πr²E

• (πr² + πl²) E

The electric flux for Gaussian surface A that enclose the charged particles in free space is (given q₁ = −14 nC, q₂ = 78.85 nC, q₃ = − 56 nC)

• 10³ Nm²C^-1

• 10³ CN^-1m^-2

• 632 × 10³ Nm²C^-1

• 632 × 10³ CN^-1m^-2

The work done in carrying a charge q once round a circle of radius r with a charge Q at the centre is

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

• $\frac{\mathrm{qQ}}{4{{\mathrm{\pi \epsilon }}_0}^2{\mathrm{r}}^2}$

• $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0{\mathrm{r}}^2}$

• None of these

Identify the wrong statement in the following. Coulomb's law correctly described the electric force that

• binds the electrons of an atom to its nucleus

• binds the protons and neutrons in the nucleus of an atom

• binds atoms together to form molecules

• binds atoms and molecules to form solids

68.

A Gaussian sphere encloses an electric dipole within it. The total flux across the sphere is

• zero

• half that due to a single charge

• double that due to a single charge

• dependent on the position of the dipole

A comb run through one's dry hair attracts small bits of paper. This is due to

• comb is a good conductor

• paper is a good conductor

• the atoms in the paper get polarised by the charged comb

• the comb possesses magnetic properties

The specific charge of a proton is 9.6 × 10⁷ C kg^-1. The specific charge of an alpha particle will be

• 9.6 × 10⁷ C kg^-1

• 19.2 × 10⁷ C kg^-1

• 4.8 × 10⁷ C kg^-1

• 2.4 × 10⁷ C kg^-1