Additional Questions - Chapter 1 Electrostatics 12th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Additional Questions Solved
I. Multiple Choice Questions
Question 1.
When a solid body is negatively charged by friction, it means that the body has
(a) acquired excess of electrons
(b) lost some, problems
(c) acquired some electrons and lost a lesser number of protons
(d) lost some positive ions
Answer:
(a) acquired excess of electrons
Question 2.
A force of $0.01 \mathrm{~N}$ is exerted on a charge of $1.2 \times 10^{-5} \mathrm{G}$ at a certain point. The electric field at that point is
(a) $5.3 \times 10^4 \mathrm{NC}^{-1}$
(b) $8.3 \times 10^{-4} \mathrm{NC}^{-1}$
(c) $5.3 \times 10^2 \mathrm{NC}^{-1}$
(d) $8.3 \times 10^4 \mathrm{NC}^{-1}$
Answer:
(d) $8.3 \times 10^4 \mathrm{NC}^{-1}$

Hint:
$
\mathrm{E}=\frac{F}{q}=\frac{0.01}{1.2 \times 10^{-5}}=8.3 \times 10^2 \mathrm{NC}^{-1}
$
Question 3 .
The electric field intensity at a point $20 \mathrm{~cm}$ away from a charge of $2 \times 105 \mathrm{C}$ is
(a) $4.5 \times 10^6 \mathrm{NC}^{-1}$
(b) $3.5 \times 10^5 \mathrm{NC}^{-1}$
(c) $3.5 \times 10^6 \mathrm{NC}^{-1}$
(d) $4.5 \times 10^5 \mathrm{NC}^{-1}$
Answer:
(a) $4.5 \times 10^6 \mathrm{NC}^{-1}$
Hint:
$
\mathrm{E}=\frac{q}{4 \pi \varepsilon_0 r^2}=\frac{9 \times 10^9 \times 2 \times 10^{-5}}{(0.2)^2}=4.5 \times 10^6 \mathrm{NC}^{-1}
$
Question 4.
How many electrons will have a charge of one coulomb?
(a) $6.25 \times 10^{18}$
(b) $6.25 \times 10^{19}$
(c) $1.6 \times 10^{18}$
(d) $1.6 \times 10^{19}$
Answer:
(a) $6.25 \times 10^{18}$
Hint:
Number of electron, $\mathrm{n}=\frac{q}{e}=\frac{1}{1.6 \times 10^{-19}}=6.25 \times 10^{18}$

Question 5 .
The ratio of the force between two charges in air and that in a medium of dielectric constant $\mathrm{K}$ is
(a) $\mathrm{K}: 1$
(b) $1: \mathrm{K}$
(c) $\mathrm{K}^2: 1$
(d) $1: \mathrm{K}^2$
Answer:
(a) $\mathrm{K}: 1$
Question 6.
The work done in moving a positive charge on an equipotential surface is
(a) finite and positive
(b) infinite
(c) finite and negative
(d) zero
Answer:
(d) zero
Question 7.
If a charge is moved against the coulomb force of an electric field.
(a) work is done by the electric field

(b) energy is used from some outside source
(c) the strength of the field is decreased
(d) the energy of the system is decreased
Answer:
(b) energy is used from some outside source
Question 8.
No current flows between two charged bodies when connected
(a) if they have the same capacitance
(b) if they have same quantity of charge
(c) if they have the same potential
(d) if they have the same charge density
Answer:
(c) if they have the same potential
Question 9.
Electric field lines about a negative point charge are
(a) circular, anticlockwise
(b) circular, clockwise
(c) radial, inwards
(d) radial, outwards
Answer:
(c) radial, inwards
Question 10.
Two plates are $1 \mathrm{~cm}$ apart and the potential difference between them is $10 \mathrm{~V}$. The electric field between the plates is
(a) $10 \mathrm{NC}^{-1}$
(b) $250 \mathrm{NC}^{-1}$
(c) $500 \mathrm{~N}^{-1}$
(d) $1000 \mathrm{NC}^{-1}$
Answer:
(d) $1000 \mathrm{NC}^{-1}$
Hint:
$
\mathrm{E}=\frac{V}{d}=\frac{10}{1 \times 10^{-2}}=8.3 \times 10^2 \mathrm{NC}^{-1}
$

Question 11.
At a large distance (r), the electric field due to a dipole varies as
(a) $\frac{1}{r}$
(b) $\frac{1}{r^2}$
(c) $\frac{1}{r^3}$
(d) $\frac{1}{r^4}$
Answer:
(c) $\frac{1}{r^3}$
Question 12.
Two thin infinite parallel plates have uniform charge densities $+c$ and $-\sigma$. The electric field in the space
between then is
(a) $\frac{\sigma}{2 \varepsilon_0}$
(b) $\frac{\sigma}{\varepsilon_0}$
(c) $\frac{2 \sigma}{2 \varepsilon_0}$
(d) Zero
Answer:
(b) $\frac{\sigma}{\varepsilon_0}$
Question 13.
Two isolated, charged conducting spheres of radii $R_1$, and $R_2$ produce the same electric field near their surfaces. The ratio of electric potentials on their surfaces is-
(a) $\frac{R_1}{R_2}$
(b) $\frac{R_2}{R_1}$
(c) $\frac{R_1^2}{R_2^2}$
(d) $\frac{R_2^2}{R_1^2}$
Answer:
(b) $\frac{R_2}{R_1}$

Question 14.
A $100 \mu \mathrm{F}$ capacitor is to have an energy content of $50 \mathrm{~J}$ in order to operator a flash lamp. The voltage required to charge the capacitor is
(a) $500 \mathrm{~V}$
(b) $1000 \mathrm{~V}$
(c) $1500 \mathrm{~V}$
(d) $2000 \mathrm{~V}$
Answer:
(b) $1000 \mathrm{~V}$
Hint:
$
\mathrm{U}=\frac{1}{2} \Rightarrow \mathrm{V}=\sqrt{\frac{2 \mathrm{U}}{\mathrm{C}}}=\frac{\sqrt{2 \times 50}}{100 \times 10^{-6}}=1000 \mathrm{~V}
$
Question 15.
A $1 \mu \mathrm{F}$ capacitor is placed in parallel with a $2 \mu \mathrm{F}$ capacitor across a $100 \mathrm{~V}$ supply. The total charge on the system is
(a) $\frac{100}{3} \mu \mathrm{C}$
(b) $100 \mu \mathrm{C}$
(c) $150 \mu \mathrm{C}$
(d) $300 \mu \mathrm{C}$
Answer:
(d) $300 \mu \mathrm{C}$
Hint:
Equivalent capacitor $=1+2=3 \mu \mathrm{F}$
Total charge, $\mathrm{q}=\mathrm{CV}=3 \times 100=300 \mu \mathrm{F}$

Question 16.
A parallel plate capacitor of capacitance $100 \mu \mathrm{F}$ is charged to $500 \mathrm{~V}$. The plate separation is then reduce to half its original value. Then the potential on the capacitor becomes
(a) $250 \mathrm{~V}$
(b) $500 \mathrm{~V}$
(c) $1000 \mathrm{~V}$
(d) $2000 \mathrm{~V}$
Answer:
(a) $250 \mathrm{~V}$
Hint:
Here, $C^{\prime}=2 C$, since the charge remains the same.
$
\mathrm{q}=\mathrm{C}^{\prime} \mathrm{V} '=\mathrm{CV} \Rightarrow \mathrm{V}=\frac{C V}{2 C}=\frac{500}{2}=250 \mathrm{~V}
$
Question 17.
A point charge $\mathrm{q}$ is placed at the midpoint of a cube of side $L$. The electric flux emerging from the cube is ${ }^2$
(a) $\frac{q}{\varepsilon_0}$
(b) $\frac{q}{6 L \varepsilon_0}$
(c) $\frac{6 L q}{\varepsilon_0}$
(d) zero
Answer:
(a) $\frac{q}{\varepsilon_0}$
Question 18.
The capacitor $\mathrm{C}$ of a spherical conductor of radius $\mathrm{R}$ is proportional to
(a) $\mathrm{R}^2$
(b) $\mathrm{R}$
(c) $\mathrm{R}^{-1}$
(d) $\mathrm{R}^0$
Answer:
(b) $\mathrm{R}$

Question 19.
Energy of a capacitor of capacitance $\mathrm{C}$, when subjected to a potential $\mathrm{V}$, is given by
(a) $\frac{1}{2} \mathrm{CV}^2$
(b) $\frac{1}{2} \mathrm{C}^2 \mathrm{~V}$
(c) $\frac{1}{2} \mathrm{CV}$
(d) $\frac{1}{2} \frac{C}{V}$
Answer:
(a) $\frac{1}{2} \mathrm{CV}^2$
Question 20.
The electric field due to a dipole at a distance $\mathrm{r}$ from its centre is proportional to
(a) $\frac{1}{r^{3 / 2}}$
(b) $\frac{1}{r^3}$
(c) $\frac{1}{r}$
(d) $\frac{1}{r^3}$
Answer:
(b) $\frac{1}{r^3}$
Question 21.
A point charge $\mathrm{q}$ is rotating around a charge $\mathrm{Q}$ in a circle of radius $r$. The workdone on it by the coulomb force is
(a) $2 \pi \mathrm{rq}$
(b) $2 \pi \mathrm{Qq}$
(c) $\frac{Q}{2 \varepsilon^0 r}$
(d) zero
Answer:
(d) zero

Question 22.
The workdone in rotating an electric dipole of moment $P$ in an electric field $E$ through an angle 0 from the direction of the field is
(a) $\mathrm{pE}(1-\cos \theta)$
(b) $2 \mathrm{pE}$
(c) zero
(d) $-\mathrm{pE} \cos \theta$
Answer:
(a) $\mathrm{pE}(1-\cos \theta)$
Hint:
$
\begin{aligned}
& \mathrm{W}=\mathrm{pE}\left(\cos \theta_0-\cos \theta\right) \\
& {\left[\theta_0=\cos 0, \cos 0=1\right]} \\
& \mathrm{W}=\mathrm{pE}(1-\cos \theta)
\end{aligned}
$
Question 23.
Capacitance of a parallel plate capacitor can be increased by
(a) increasing the distance between the plates
(b) increasing the thickness of the plates
(c) decreasing the thickness of the plates
(d) decreasing the distance between the plates
Answer:
(d) decreasing the distance between the plates
Question 24.
Two charges are placed in vacuum at a distance $\mathrm{d}$ apart. The force between them is $\mathrm{F}$. If a medium of dielectric constant 2 is introduced between them, the force will now be
(a) $4 \mathrm{~F}$
(b) $2 \mathrm{~F}$
(c) $\mathrm{F} / 2$
(d) $\mathrm{F} / 4$
Answer:
(d) $\mathrm{F} / 4$

Question 25.
An electric charge is placed at the centre of a cube of side a. The electric flux through one of its faces will be
(a) $\frac{q}{6 \varepsilon^0}$
(b) $\frac{q}{\varepsilon_0 a^2}$
(c) $\frac{q}{4 \pi \varepsilon_0 a^2}$
(a) $\frac{q}{\varepsilon^0}$
Answer:
(a) $\frac{q}{6 \varepsilon^0}$
Hint:
According to Gauss's law, the electric flux through the cube is $\frac{q}{\varepsilon^0}$. Since there are six faces, the flux through one face is $\frac{q}{6 \varepsilon^0}$.
Question 26.
The electric field in the region between two concentric charged spherical shells-
(a) is zero
(b) increases with distance from centre
(c) is constant
(d) decreases with distance from centre
Answer:
(d) decreases with distance from centre
Question 27.
A hollow metal sphere of radius $10 \mathrm{~cm}$ is charged such that the potential on its surface is $80 \mathrm{~V}$. The potential at the centre of the sphere is-
(a) $800 \mathrm{~V}$
(b) zero
(c) $8 \mathrm{~V}$
(d) $80 \mathrm{~V}$
Answer:
(d) $80 \mathrm{~V}$
Question 28.
A $4 \mu \mathrm{F}$ capacitor is charged to $400 \mathrm{~V}$ and then its plates are joined through a resistance of $1 \mathrm{~K} \Omega$. The heat produced in the resistance is-
(a) $0.16 \mathrm{~J}$
(b) $0.32 \mathrm{~J}$
(c) $0.64 \mathrm{~J}$
(d) $1.28 \mathrm{~J}$
Answer:
(b) $0.32 \mathrm{~J}$

Hint:
The energy stored in capacitor is converted into heat
$
\mathrm{U}=\mathrm{H}=\frac{1}{2} \mathrm{CV}^2=\frac{1}{2} \times 4 \times 10^{-6} \times(400)^2=0.32 \mathrm{~J}
$
Question 29.
The workdone in carrying a charge $\mathrm{Q}$, once round a circle of radius $\mathrm{R}$ with a charge $\mathrm{Q}_2$ at the centre is-
(a) $\frac{Q_1 Q_2}{4 \pi \varepsilon_0 \mathrm{R}^2}$
(b) zero
(c) $\frac{Q_1 Q_2}{4 \pi \varepsilon_0 \mathrm{R}}$
(d) infinite
Answer:
(b) zero
Hint:
The electric field is conservative. Therefore, no work is done in moving a charge around a closed path in a electric field.
Question 30.
Two plates are $2 \mathrm{~cm}$ apart. If a potential difference of $10 \mathrm{~V}$ is applied between them. The electric field between the plates will be
(a) $20 \mathrm{NC}^{-1}$
(b) $500 \mathrm{NC}^{-1}$
(c) $5 \mathrm{NC}^{-1}$
(d) $250 \mathrm{NC}^{-1}$
Answer:
(b) $500 \mathrm{NC}^{-1}$
Hint:
$
\frac{V}{d}=\frac{10}{2 \times 10^{-2}} 500 \mathrm{NC}^{-1}
$

Question 31.
The capacitance of a parallel plate capacitor does not depend on
(a) area of the plates
(b) metal of the plates
(c) medium between the plates
(d) distance between the plates
Answer:
(b) metal of the plates
Question 32.
A capacitor of $50 \mu \mathrm{F}$ is charged to 10 volts. Its energy in joules is
(a) $2.5 \times 10^{-3}$
(b) $5 \times 10^{-3}$
(c) $10 \times 10^{-4}$
(d) $2.5 \times 10^{-4}$
Answer:
(a) $2.5 \times 10^{-3}$
Hint:
$
\mathrm{U}=\frac{1}{2} \mathrm{CV}^2=\frac{1}{2} \times 50 \times 10^{-6} \times(10)^2=2.5 \times 10^{-3} \mathrm{~J}
$
Question 33.
A cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of the cube is
(a) $\frac{q}{b^2}$
(b) $\frac{q}{2 b^2}$
(c) $\frac{32 q}{b^2}$
(d) zero
Answer:

(d) zero
Hint:
There
is an equal charge at diagonally opposite comer. The fields due the these at the centre cancel out.
Therefore, the net field at the centre is zero.

Question 34.
Total electric fulx coming out of a unit positive charge put in air is
(a) $\varepsilon_0$
(b) $\varepsilon_0^{-1}$
(c) $\left(4 \pi \varepsilon_0\right)^{-1}$
(d) $4 \pi \varepsilon_0$
Answer:
(b) $\varepsilon_0^{-1}$
Question 35.
Electron volt (eV) is a unit of
(a) energy
(b) potential
(c) current
(d) charge
Answer:
(a) energy
Question 36.
A point $Q$ lies on the perpendicular bisector of an electric dipole of dipole moment $P$. If the distance of $Q$ from the dipole is $r$, then the electric field at $Q$ is proportional to-
(a) $\mathrm{p}^{-1}$ and $\mathrm{r}^{-2}$
(b) $\mathrm{p}$ and $\mathrm{r}^{-2}$
(c) $\mathrm{p}$ and $\mathrm{r}^{-3}$
(d) $\mathrm{p}^2$ and $\mathrm{r}^{-3}$
Answer:
(c) $\mathrm{p}$ and $\mathrm{r}^{-3}$
Question 37.
A hollow insulated conducting sphere is given a positive charge of $10 \mu \mathrm{C}$. What will be the electric field at the centre of the sphere is its radius is 2 metres?
(a) zero
(b) $8 \mu \mathrm{Cm}^{-2}$
(c) $20 \mu \mathrm{Cm}^{-2}$
(d) $5 \mu \mathrm{Cm}^{-2}$
Answer:
(d) zero

Question 38.
A particle of charge $\mathrm{q}$ is placed at rest in a uniform electric field $\mathrm{E}$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is-
(a) $\mathrm{qE}^2 \mathrm{y}$
(b) $\mathrm{q}^2 \mathrm{Ey}$
(c) $q E y^2$
(d) qEy
Answer:
(d) qEy
Hint:
Force on the particle $=\mathrm{qE}$
$\mathrm{KE}=$ Workdone by the force $=\mathrm{F} . \mathrm{y}=\mathrm{qEy}$
Question 39.
Dielectric constant of metals is-
(a) 1
(b) greater then 1
(c) zero
(d) infinite
Answer:
(d) infinite
Question 40.
When a positively charged conductor is earth connected
(a) protons flow from the conductor to the earth
(b) electrons flow from the earth to the conductor
(c) electrons flow from the conductor to the earth
(d) no charge flow occurs
Answer:
(b) electrons flow from the earth to the conductor
Question 41.
The SI unit of electric flux is
(a) volt metre 2
(b) newton per coulomb
(c) volt metre
(d) joule per coulomb
Answer:
(c) volt metre

Question 42.
Twenty seven water drops of the same size are charged to the same potential. If they are combined to form a big drop, the ratio of the potential of the big drop to that of a small drop is-
(a) 3
(b) 6
(c) 9
(d) 27
Answer:
(c) 9
Hint:
$
\begin{aligned}
& \mathrm{V}^{\prime}=\mathrm{n}^{2 / 3} \mathrm{~V} \\
& \Rightarrow \frac{V^{\prime}}{V}=(27)^{2 / 3}=9
\end{aligned}
$
Question 43.
A point charge $+\mathrm{q}$ is placed at the midpoint of a cube of side 1 . The electric flux emerging ' from the cube is-
(a) $\frac{q}{\varepsilon^0}$
(b) $\frac{6 q l^2}{\varepsilon^0}$
(c) $\frac{q}{6 l^2 \varepsilon^0}$
(d) $\frac{C^2 V^2}{2}$
Answer:
(a) $\frac{q}{\varepsilon^0}$

Question 45.
The electric potential at the centre of a charged conductor is-
(a) zero
(b) twice that on the surface
(c) half that on the surface
(d) same as that on the surface
Answer:
(d) same as that on the surface
Question 46.
The energy stored in a capacitor is given by
(a) $\mathrm{qV}$
(b) $\frac{1}{2} \mathrm{qV}$
(c) $\frac{1}{2} \mathrm{CV}$
(d) $\frac{q}{2 C}$
Answer:
(b) $\frac{1}{2} \mathrm{qV}$
Question 47.
The unit of permitivity of free space so is
(a) coulomb/newton-metre
(b) newton-metre $2 /$ coulomb $^2$
(c) coulomb ${ }^2 /$ newton-metre $^2$
(d) coulomb/(newton-metre $)^2$
Answer:
(c) coulomb ${ }^2 /$ newton-metre ${ }^2$

Question 48.
An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p$. It is placed in a uniform electric field $\mathrm{E}$. It its dipole moment is along the direction of the field, the force on it and its potential energy are, respectively.
(a) $2 \mathrm{qE}$ and minimum
(b) $\mathrm{qE}$ and $\mathrm{pE}$
(c) zero and minimum
(d) $\mathrm{qE}$ and maximum
Answer:
(c) zero and minimum
Hint:
Potential energy, $\mathrm{U}=-\mathrm{pE} \cos \theta$
For $\mathrm{q}=0^{\circ} ; \mathrm{U}=-\mathrm{pE}$, which is minimum.
Question 49.
An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\vec{E}$. The workdone in rotating the dipole by $90^{\circ}$ is
(a) $\frac{p E}{2}$
(b) $2 \mathrm{pE}$
(c) $\mathrm{pE}$
(d) $\sqrt{2 p E}$
Answer:
(c) $\mathrm{pE}$
Question 50.
Aparallel plate air capacitor is charged to a potential difference of $\mathrm{V}$ volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle.
As a result the potential difference between the plates
(a) does not charge
(b) becomes zero
(c) increases
(d) decreases
Answer:
(c) increases
Question 51.
When air is replaced by a dielectric medium of constant $K$, the maximum force of attraction between two charges separated by a distance
(a) increases $\mathrm{K}$ times
(b) increases $\mathrm{K}^{-1}$ times
(c) decreases $\mathrm{K}$ times
(d) remains constant
Answer:
(c) decreases $\mathrm{K}$ times

Question 52.
A comb run through one's dry hair attracts small bits of paper. This is due to the fact that
(a) comb is a good conductor
(b) paper is a good conductor
(c) the atoms in the paper gets polarised by the charged comb
(d) the comb posseses magnetic properties
Answer:
(c) the atoms in the paper gets polarised by the charged comb
Question 53.
Which of the following is not a property of equipotential surfaces?
(a) they do not cross each other
(b) they are concentric spheres for uniform electric field
(c) the rate of change of potential with distance on them is zero
(d) they can be imaginary spheres.
Answer:
(b) they are concentric spheres for uniform electric field
Question 54.
A charge $Q$ is enclosed by a Gaussian spherical surface of radius $R$. If the radius is doubled, then the outward electric flux will be
(a) reduced to half
(b) doubled
(c) becomes 4 times
(d) remains the same
Answer:
(d) remains the same
Question 55.
If the electric field in a region is given by $\vec{E}=5 \hat{j}+4 \hat{j}+9 \hat{k}$, then the electric flux through a surface of area 20 units lying in the $y-z$ plane will be-
(a) 20 units
(b) 80 units
(c) 100 units
(d) 180 units
Answer:
(c) 100 units
Hints:

The area vector $\vec{A}=20 \hat{j} ; \vec{E}=(5 \hat{j}+4 \hat{j}+9 \hat{k})$
Flux $(\Phi)=\vec{E}-\vec{A}=5 \times 20=100$ units
Question 56.
$\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are three points in a uniform electric field. The electric potential is-

(a) maximum at $\mathrm{A}$
(b) maximum at $\mathrm{B}$
(c) maximum at $\mathrm{B}$
(d) same at all the three points $A, B$ and $C$
Answer:
(b) maximum at $\mathrm{B}$
Hint:
The potential decreases in the direction of the field. Therefore $\mathrm{V}_{\mathrm{B}}>\mathrm{V}_{\mathrm{C}}>\mathrm{C}_{\mathrm{A}}$.

Question 57.
A conducting sphere of radius $R$ is give a charge $Q$. The electric potential and the electric field at the centre of the sphere are, respectively-
(a) zero, $\frac{Q}{4 \pi \varepsilon_0 R^2}$
(b) $\frac{Q}{4 \pi \varepsilon_0 R}$
(c) $\frac{Q}{4 \pi \varepsilon_0 R}$, zero
(d) zero,zero
Answer:
(c) $\frac{Q}{4 \pi \varepsilon_0 R}$, zero.
II. Fill in the blanks
Question 1.
A dipole is placed in a uniform electric field with its axis parallel to the field. It experiences .............
Answer:
neither a net force nor a torque
Question 2.
The unit of permittivity is ..........
Answer:
$\mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$
Question 3.
The branch of physics which deals with static electric charges or charges at rest is ........
Answer:
electrostatics
Question 4.
The charges in a electrostatics field are analogous to ...........  in a gravitational field.
Answer:
mass
Question 5. 
The substances which acquire charges on rubbing are said to be .................
Answer:
electrified

Question 6.
Electron means ........
Answer:
amber
Question 7.
A glass rod rubbed with a silk cloth. Glass rod and silk cloth acquires ..............
Answer:
positive and negative charge respectvely.
Question 8.
When ebonite rod is rubbed with fur, ebonite rod and fur acquires .................
Answer:
negative and positive charge respectively
Question 9.
................. termed the classification of positive and negative charges.
Answer:
Franklin
Question 10.
Applications such as electrostatic point spraying and powder coating, are based on the property of ........................ between charged bodies.
Answer:
attraction and repulsion
Question 11.
Bodies which allow the charge to pass through them are called ..............
Answer:
conductor
Question 12.
Bodies which do not allow the charge to pass through them are called ..............
Answer:
insulators

Question 13.
The unit of electric charge is ............
Answer:
coulomb
Question 14.
Total charge in an isolated sysem ..................
Answer:
remains a constant
Question 15.
The force between two charged bodies was studied by ...................
Answer:
coulomb
Question 16.
The unit of permittivity in free space $(\mathrm{s} 0)$ is ..............
Answer:
$
\mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}
$
Question 17.
The value of s, for air or vacuum is ....................
Answer: 1
Question 18.
Charges can neither be created nor be destroyed is the statement of law of conservation of ...................
Answer:
charge
Question 19.
The space around the test charge, in which it experiences a force is known as field .............
Answer:
electric

Question 20 .
Electric field at a point is measued in terms of .................
Answer:
electric field intensity
Question 21.
The unit of electric field in tensity is .................
Answer:
$\mathrm{NC}^{-1}$
Question 22.
The lines of force are far apart, when electric field $E$ is .............
Answer:
small
Question 23.
The lines of force are close together, when electric field $E$ is ...................
Answer:
large
Question 24.
Electric dipole moment ...........
Answer:
$\mathrm{P}=2 \mathrm{qd}$
Question 25.
Torque experienced by electric dipole is ..................
Answer:
$\mathrm{x}=\mathrm{PE} \sin \theta$
Question 26.
An electric dipole placed in a non-uniform electric field at an angle 0 experiences ..................
Answer:
both torque and force
Question 27.
When thee dipole is aligned parallel to the field, its electric potential energy is .................
Answer:
$\mathrm{u}=-\mathrm{PE}$

Question 28.
Change of potential with distance is known as ......................
Answer:
potential distance
Question 29.
The number of electric lines of force crossing through the given area is .................
Answer:
electric flux
Question 30 .
The process of isolating a certain region of space from external field is called................
Answer:
electrostatic shielding
Question 31.
Capacitor is a device to store ...............
Answer:
charge
Question 32.
The charge density in maximum at...............
Answer:
pointed
Question 33.
The principle made use of in lightning arrestor is.................
Answer:
action of points
Question 34.
Van de Graaff generator producers large electrostatic potential difference of the order of..............
Answer: 
$10^7 \mathrm{~V}$
III. Match the following
Question 1.

Answer:
(i) $\rightarrow$ (d)
(ii) $\rightarrow$ (a)
(iii) $\rightarrow$ (b)
(iv) $\rightarrow$ (c)
Question 2.

Answer:
(i) $\rightarrow$ (c)
(ii) $\rightarrow$ (d)
(iii) $\rightarrow$ (a)
(iv) $\rightarrow$ (b)
Question 3.

Answer:
(i) $\rightarrow$ (b)
(ii) $\rightarrow$ (d)
(iii) $\rightarrow$ (a)
(iv) $\rightarrow$ (c)
Question 4.

Answer:
(i) $\rightarrow$ (b)
(ii) $\rightarrow(\mathrm{d})$
(iii) $\rightarrow$ (a)
(iv) $\rightarrow$ (c)
IV. Assertion and reason type
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but the reason is not correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Question 1.
Assertion: Electric lines of force cross each other.
Reason: Electric field at a point supermpose to give one resultant electric field.

Answer:
(e) Both assertion and reason are true but the reason is not correct explanation of the assertion. Explanation: If electric lines of forces cross each other, then the electric field at the point of intersection will have two direction simultaneously which is not possible physically.
Question 2.
Assertion: Charge is quantized.
Reason: Charge, which is less than $1 \mathrm{C}$ is not possible.
Answer:
(c) If assertion is true but reason is false.
Explanation: $\mathrm{Q}= \pm$ ne and charge lesser than $1 \mathrm{C}$ is possible.
Question 3.
Assertion:
A point charge is brought in an electric field. The field at a nearby point will increase, whatever be the nature of the charge.
Reason: The electric field is independent of the nature of charge.
(d) If the assertion and reason both are false.
Explanation: Electric field at the nearby-point will be resultant of existing field and field due to the charge brought. It may increase or decrease if the charge is positive or negative depending on the position of the point with respect to the charge brought.
Question 4.
Assertion: The tyre's of aircraft's are slightly conducting.
Reason: If a conductor is connected to ground, the extra charge induced on conductor will flow to ground.
Answer:
(b) Both assertion and reason are true but the reason is not correct explanation of the assertion. Explanation: During take off and landing, the friction between treys and the run way may cause electrification of treys. Due to conducting to a ground and election sparking is avoided.
Question 5.
Assertion: The lightening conductor at the top of a high building has sharp ends.
Reason: The surface density of charge at sharp points is very high, resulting in setting up of electric wind.
Answer:
(a) Both assertion and reason are true and the reason is the correct explanation of the assertion.

Short Answer Questions
Question 1.
What is meant by triboelectric charging?
Answer:
Charging the objects through rubbing is called triboelectric charging.
Question 2.
What is meant by conservation of total charges?
Answer:
The total electric charge in the universe is constant and charge can neither be created nor be destroyed. In any physical process, the net change in charge will always be zero.
Question 3.
State Gauss's Law?
Answer:
Definition:
Gauss's law states that if a charge $Q$ is enclosed by an arbitrary closed surface, then the total electric flux OE through the closed surface is
$
\Phi_{\mathrm{E}}=\oint \vec{E} \cdot \mathrm{d} \vec{A}=\frac{q_{\text {end }}}{\varepsilon_0}
$
Question 4.
What is meant by electrostatic shielding?
During lightning accompanied by a thunderstorm, it is always safer to sit inside a bus than in open ground or under a tree. The metal body of the bus provides electrostatic shielding, since the electric field inside is zero. During lightning, the charges flow through the body of the conductor to the ground with no effect on the person inside that bus.
Question 5.
What is meant by dielectric?
Answer:
A dielectric is a non-conducting material and has no free electrons. The electrons in a dielectric are bound within the atoms. Ebonite, glass and mica are some examples of dielectrics.
Question 6.
What are non-polar molecules? Give examples.

Answer:
A non-polar molecule is one in which centers of positive and negative charges coincide. As a result, it has no permanent dipole moment. Examples of non-polar molecules are hydrogen $\left(\mathrm{H}_2\right)$, oxygen $\left(\mathrm{O}_2\right)$, and carbon dioxide $\left(\mathrm{CO}_2\right)$ etc.

Question 7.
What are polar molecules? Give examples.
Answer:
In polar molecules, the centers of the positive and negative charges are separated even in the absence of an external electric field. They have a permanent dipole moment.
The net dipole moment is zero in the absence of an external electric field. Examples of polar molecules are $\mathrm{H}_2 \mathrm{O}, \mathrm{N}_2 \mathrm{O}, \mathrm{HCl}, \mathrm{NH}_3$.
Question 8.
What is a capacitors?
Answer:
Capacitor is a device used to store electric charge and electrical energy. Capacitors are widely used in many electronic circuits and have applications in many areas of science and technology.
Long Answer Questions
Question 1.
Derive an expression for electric field due to the system of point charges?
Answer:
Electric field due to the system of point charges:
Suppose a number of point charges are distributed in space. To find the electric field at some point $\mathrm{P}$ due to this collection of point charges, superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. This is called superposition of electric fields.
Consider a collection of point charges $q_1, q_2, q_3, \ldots ., q_n$ located at various points in space. The 'total electric field at some point $P$ due to all these $\mathrm{n}$ charges is given by
$
\begin{aligned}
& \overrightarrow{\mathrm{E}}_{\mathrm{tot}}=\overrightarrow{\mathrm{E}}_1+\overrightarrow{\mathrm{E}}_2+\overrightarrow{\mathrm{E}}_3+\ldots .+\overrightarrow{\mathrm{E}}_n \\
& \overrightarrow{\mathrm{E}}_{\mathrm{tot}}=\frac{1}{4 \pi \varepsilon_0}\left\{\frac{q_1}{q_{1 \mathrm{P}}^2} \hat{r}_{1 \mathrm{P}}+\frac{q_2}{q_{2 \mathrm{P}}^2} \hat{r}_{2 \mathrm{P}}+\frac{q_3}{q_{3 \mathrm{P}}^2} \hat{r}_{3 \mathrm{P}}+\ldots .+\frac{q_n}{q_{\mathrm{nP}}^2} \hat{r}_{\mathrm{nP}}\right\}
\end{aligned}
$
Here $r_{1 p}, r_{2 p}, r_{3 p}, \ldots, r_{n p}$, are the distance of the charges ${ }_1, q_2, q_3, \ldots, q_n$ from the point respectively. Also $\hat{r}_{1 \mathrm{p}}+\hat{r}_{2 \mathrm{p}}+\hat{r}_{3 \mathrm{p}}, \ldots ., \hat{r}_{\mathrm{np}}$ are the corresponding unit vectors directed from $\mathrm{q}_1, \mathrm{q}_2, \mathrm{q}_3, \ldots, \mathrm{q}_{\mathrm{n}}$ tpo $\mathrm{P}$.

Equation (2) can be re-written as,
$
\overrightarrow{\mathrm{E}}_{\mathrm{tot}}=\frac{1}{4 \pi \varepsilon_0} \sum_{i=1}^n\left(\frac{q_i}{q_{i \mathrm{p}}^2} \hat{r}_{\mathrm{ip}}\right)
$
For example in figure, the resultant electric field due to three point charges $q_1, q_2, q_3$ at point $P$ is shown. Note that the relative lengths of the electric field vectors for the charges depend on relative distantes of the charges to the point $P$.
Question 2.
Derive an expression for electric flux of rectangular area placed in uniform electric field. Answer:
(i) Electric flux for uniform Electric field:
Consider a uniform electric field in a region of space. Let uschoose an area A normal to the electric field lines as shown in figure (a). The electric flux for this case is $\Phi_{\mathrm{E}}=\mathrm{EA} \ldots .(1)$
Suppose the same area $A$ is kept parallel to the uniform electric field, then no electric field lines pierce through the area $\mathrm{A}$, as shown in figure (b). The electric flux for this case is zero. $\Phi_{\mathrm{E}}=0 \ldots$. (2)
If the area is inclined at an angle $\theta$ with the field, then the component of the electric field perpendicular to the area alone contributes to the electric flux. The electric field component parallel to the surface area will not contribute to the electric flux. This is shown in figure (c). For this case, the electric flux $\Phi \mathrm{E}=(\mathrm{E} \cos \theta) \mathrm{A} \ldots(3)$
Further, $\theta$ is also the angle between the electric field and the direction normal to the area. Hence in general, for uniform electric field, the electric flux is defined as
$
\Phi_{\mathrm{E}}=\vec{E} \cdot \vec{A}=\mathrm{EA} \cos \theta
$

Here, note that $\vec{A}$ is the area vector $\vec{A}=\mathrm{A} \hat{n}$. Its magnitude is simply the area A and the direction is along the unit vector h perpendicular to the area. Using this definition for flux, $\Phi_{\mathrm{E}}=\vec{E} \cdot \vec{A}$, equations (2) and (3) can be obtained as special cases.
In figure (a), $\theta=0^{\circ}$ so $\Phi_{\mathrm{E}}=\vec{E} \cdot \vec{A}=\mathrm{EA}$
In figure (b), $\theta=90^{\circ}$ so $\Phi_{\mathrm{E}}=\vec{E} \cdot \vec{A}=0$
(ii) Electric flux in a non uniform electric field and an arbitrarily shaped area: Suppose the electric field' is not uniform and the area $\mathrm{A}$ is not flat, then the entire area is divided into $\mathrm{n}$ small area segments $\Delta \vec{A}_1 \Delta \vec{A}_2, \Delta \vec{A}_3, \ldots . \Delta \vec{A}_{\mathrm{n}}$, such that each area element is almost flat and the electric field over each area element is considered to be uniform. The electric flux for the entire area $\mathrm{A}$ is approximately written as
$
\begin{aligned}
& \Phi_{\mathrm{E}}=\overrightarrow{\mathrm{E}}_1 \cdot \Delta \overrightarrow{\mathrm{A}}_1+\overrightarrow{\mathrm{E}}_2 \cdot \Delta \overrightarrow{\mathrm{A}}_2+\overrightarrow{\mathrm{E}}_3 \cdot \Delta \overrightarrow{\mathrm{A}}_3+\cdots+\overrightarrow{\mathrm{E}}_n \\
& \Delta \overrightarrow{\mathrm{A}}_n=\sum_{i=1}^n \overrightarrow{\mathrm{E}}_i \cdot \Delta \overrightarrow{\mathrm{A}}_i \ldots(5)
\end{aligned}
$
By taking the limit $\Delta \vec{A}_1 \rightarrow 0$ (for all i) the summation in equation (5) becomes integration. The total electric flux for the entire area is given by
$
\Phi_{\mathrm{E}}=\int \vec{E} \cdot \mathrm{d} \vec{A} \ldots .(6)
$
From Equation (6), it is clear that the electric flux for a given surface depends on both the electric field pattern on the surface area and orientation of the surface with respect to the electric field.
(iii) Electric flux for closed surfaces: In the previous section, the electric flux for any arbitrary curved surface is discussed. Suppose a closed surface is present in the region of the non-uniform electric field as shown in figure (a).

The total electric flux over this closed surface is written as
$$
\Phi_{\mathrm{E}}=\oint \vec{E} \cdot \mathrm{d} \vec{A}
$$
Note the difference between equations (6) and (7). The integration in equation (7) is a closed surface integration and for each areal element, the outward normal is the direction of $\mathrm{d} \vec{A}$ as shown in the figure (b).
The total electric flux over a closed surface can be negative,
positive or zero. In the figure (b), it is shown that in one area element, the angle between $\mathrm{d} \vec{A}$ and $\vec{E}$ is less than $90^{\circ}$, then the electric flux is positive and in another areal element, the angle between $\mathrm{dA}$ and $\mathrm{E}$ is greater than $90^{\circ}$, then the electric flux is negative. In general, the electric flux is negative if the electric field lines enter the closed surface and positive if the electric field lines leave the closed surface.