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Dielectric substances and polarization - class-XII

Description: dielectric substances and polarization
Number of Questions: 50
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Tags: electrostatic potential and capacitance electrostatics physics
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Dielectric constant for a metal is:

  1. zero

  2. infinite

  3. 1

  4. 10


Correct Option: B
Explanation:

Permittivity of metals is very high comparable to the permittivity of free space. So dielectric constant for metal is infinite.

A parallel plate condenser of capacity $10\mu F$ is connected to an A.C. supply voltage $e = 4\sin \left( {100\pi t} \right)$. The maximum displacement current:

  1. $4\pi \mu A$

  2. $4\pi mA$

  3. $2.8\pi \mu A$

  4. $2\pi \mu A$


Correct Option: B
Explanation:

Displacement current, ${i _d} = {\varepsilon _ \circ }A\frac{{dE}}{{dt}}$
where, $A$ is area and $E$ is electric field
$\begin{array}{l}E = \frac{e}{d} = \frac{{4\sin (100\pi t)}}{d}\{i _d} = {\varepsilon _ \circ }A \times \frac{1}{d}\left[ {\frac{d}{{dt}}\left( {4\sin 100\pi t} \right)} \right]\ = \frac{{{\varepsilon _ \circ }A}}{d}.4(cos100\pi t) \times 100\pi \ = C.400\pi .cos100\pi t\{\left( {{i _d}} \right) _{\max }} = \left( {10 \times {{10}^{ - 6}}} \right) \times 400\pi A\ = 4\pi  \times {10^{ - 3}}A = 4\pi mA\end{array}$

Which of the following can be used as dielectric?

  1. Plastics

  2. Mica

  3. Porcelain

  4. All of the above


Correct Option: D
Explanation:

The dielectric is a material through which no electric current passes. Here the given materials-plastic, mica and porcelain are all the  dielectric because current can not pass through them.

Which of the following is/are non-polar dielectrics?

  1. $HCL$

  2. Water

  3. Benzene

  4. $NH _3$


Correct Option: C
Explanation:

Ammonia and $HCl$ are polar molecules since they have a net dipole moment towards a particular direction. Both water and benzene are non-polar molecules. But water is a conductor of electricity, whereas benzene is a dielectric (insulator).

Breakdown voltage is
$A$. voltage at which dielectric behaves as conductor
$B$. voltage at which molecules starts flowing inside the dielectric freely.
Which of the following is correct regarding above case,

  1. Both $B$, $A$ are correct

  2. $B$ is correct

  3. $A$ is correct

  4. None of the above is correct


Correct Option: B
Explanation:

Breakdown voltage for a dielectric is the maximum voltage at which, applied electric field becomes so high that electrons break up from the molecules of dielectric and becomes free inside the dielectric due to this dielectric becomes conductive. 

Which of the following statement is false in context of dielectric?

  1. Materials of polar molecules have higher dielectric constant.

  2. Materials of polar molecules have lower dielectric constant.

  3. Materials of polar molecules have higher breakdown voltage.

  4. Materials of polar molecules have lower breakdown voltage.


Correct Option: A,D

If $C$ is the value of the capacitance of a capacitor filled with a given dielectric and $a$ is the capacitance of an identical capacitor in a vacuum, the dielectric constant, symbolized by the Greek letter kappa, , is simply expressed as

  1. $\dfrac{C}{a}$

  2. $\dfrac{a}{C}$

  3. $C\times a$

  4. None 


Correct Option: A
Explanation:

The capacitance of a parallel plate capacitor filled with the given material of dielectric constant $\kappa$ is given by:

              $C=\dfrac{\kappa\varepsilon _{0}A}{d}$ .....................eq1
And the capacitance of the same capacitor without the given material is given by:
              $a=\dfrac{\varepsilon _{0}A}{d}$  .....................eq2
Dividing eq1 by eq2:
              $C/a=\kappa$

The value of the dielectric constant at room temperature (25 C, or 77 F) for air is 

  1. $1.00059 $

  2. $2.00059 $

  3. $0.0009 $

  4. $0.00059 $


Correct Option: A
Explanation:

The value of dielectric constant for air at room temperature $ (25^{o}C , or 77^{o}F )$ is $1.00059$ .

Which of the following is polar dielectrics?

  1. $HCL$

  2. $NH _3$

  3. $H _2O$

  4. All of the above


Correct Option: D
Explanation:

Polar dielectric are those in which center of positive and negative charge is not same due to their shapes. 

$HCl$ , $NH _{3}$ and $H _{2}O$ all are polar dielectrics due to their high dielectric constant formed due to the difference in the polarity.

The insertion of a dielectric between the plates of a parallel-plate capacitor always 

  1. increases its capacitance 

  2. decreases its capacitance 

  3. remains same its capacitance 

  4. none of the above 


Correct Option: A
Explanation:

The capacitance of a parallel plate capacitor completely filled with a given material of dielectric constant $K$ is given by:

              $C=\dfrac{K\varepsilon _{0}A}{d}$ .....................eq1
And the capacitance of the same capacitor without the given material is given by:
              $C'=\dfrac{\varepsilon _{0}A}{d}$  .....................eq2
Dividing eq1 by eq2:
              $C/C'=K$
As $K>1$ always, hence $C>C'$ i.e. the insertion of a dielectric between the plates of a parallel -plate capacitor always increases the capacitance.

The value of the static dielectric constant of any material is always 

  1. greater than 1

  2. equal to 1

  3. lesser than 1 

  4. None 


Correct Option: A
Explanation:

Dielectric constant or relative permittivity is the materialistic property of any material .Relative permittivity of a material is the ratio of permittivity of the material to the permittivity of free space,

              $\varepsilon _{r}=\dfrac{\varepsilon}{\varepsilon _{0}}$
As $\varepsilon>\varepsilon _{0}$, because permittivity of free space is lowest, therefore $\varepsilon _{r}(or K)>1$

The slight separation of charge, or polarization

  1. reduces the electric field within the dielectric.

  2. increases the electric field within the dielectric.

  3. doesn't effect the electric field within the dielectric.

  4. none of the above


Correct Option: A
Explanation:

Electric field intensity is inversely proportional to the square of the distance between the point under consideration and the charge. Hence, electric field reduces when the charge moves away or gets separated. When a dielectric is polarized,  negative charge get attracted towards the source of the electric field and positive charge gets repelled from the source. The dipole of the dielectrics get aligned in a direction opposite to the electric field. This produces a  reverse electric field and the intensity of the applied electric field reduces .

Which of the following is not dielectric materials?

  1. Silicon dioxide

  2. Silicon nitride 

  3. Titanium oxide

  4. None of the above


Correct Option: D
Explanation:

All the given materials are very good conductors having high value of dielectric constant. Silicon dioxide is used in MOSFET, silicon nitride in VLSI (very large scale integration) fabrication of IC and titanium oxide in ceramics.

State whether given statement is True or False
The dielectric constant is the ability of a material to establish an electric field.

  1. True

  2. False


Correct Option: A
Explanation:

We know that Dielectric material refers to nonconductors or insulators in which an electric field can be sustained with a minimum dissipation of power.

And the dielectric constant is the ability of a material to establish an electric field.
Therefore, Given statement is true.

The value of relative permittivity of air is

  1. $8.854\times { 10 }^{ -12 }{ C }^{ 2 }{ N }^{ -1 }{ m }^{ -2 }$

  2. $9\times { 10 }^{ 9 }{ C }^{ 2 }{ N }^{ -1 }{ m }^{ -2 }$

  3. $1$

  4. $8.854\times { 10 }^{ 12 }$


Correct Option: C
Explanation:

The relative permittivity of a material is ratio of its (absolute) permittivity to the permittivity of vacuum. For air it is almost 1. 

A plane electromagnetic wave in a non magnetic dielectric medium is given by $\bar{E} = \bar{E _0} ( 4 \times 10^{-7} \times - 50 t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

  1. 2.4

  2. 5.8

  3. 8.2

  4. 4.8


Correct Option: B
Explanation:

Given equation of wave 

$\vec{E} = \vec{E} _0 (4 \times \vec{10} x - 50 t)$
Comparing with general equation of wave,
$\vec{E} = \vec{E} _0 (kx - wt),$
we get,
$w = 50\ rad/s.$   $k = 4 \times 10^{-7} m^{-1}$
Thus velocity of wave, 
$v = \dfrac{w}{k} = \dfrac{50}{4 \times 10^{-7}} = 1.25 \times 10^8 m/s$
so, refractive index of medium,
$\mu = \dfrac{e}{v} = \dfrac{3 \times 10^8}{1.25 \times 10^8} = 2.4$
using, 
$u^2 = km.ke$     [km and ke are magnetic and dielectric di - constants]
as medium is non diamagnetic, $km = 1$
$\Rightarrow ke = \mu^2 = (2.4)^2 \Rightarrow ke = 5.76$

The velocity factor of a transmission line is $0.62$. Calculate dielectric constant of the insulation used

  1. $2.6$

  2. $3$

  3. $4$

  4. $5$


Correct Option: A
Explanation:
Here, V.F. = 0.62, k = ?
As $k=\dfrac { 1 }{ { \left( V.F. \right)  }^{ 2 } } \therefore k=\dfrac { 1 }{ { \left( 0.62 \right)  }^{ 2 } } =2.6.$

Two charges placed in air repel each other by a force of $10^{-4}N$. When  oil is introduced between the charges, the force becomes $2.5 \times 10^{-5} N$. The dielectric constant of oil is: 

  1. $2.5$

  2. $0.25$

  3. $2.0$

  4. $4.0$


Correct Option: D

The dielectric constant $k$ of a medium can be defined as $k=M/N$, where $N$ is the capacity of a parallel plate capacitor. When the space between plates is filled with air, $M$ is ?

  1. the charge of the capacitor

  2. the capacity of a parallel plate capacitor with a dielectric between the plates

  3. the dielectric intensity in the space between the plates

  4. the P.D. across the plates of the condenser, with a dielectric between them


Correct Option: C

$64$ small drops of mercury each of radius $r$ and change $q$ coalesce to from a big drop. The ratio of the surface charge density of each small drop with that of big drop is:

  1. $4:1$

  2. $1:4$

  3. $1:64$

  4. $64:1$


Correct Option: B
Explanation:
Formulae:

$\dfrac{\sigma _{small} }{\sigma _{big} }=\dfrac{q}{Q} \times \dfrac{R^2}{r^2}$

$=\dfrac{q}{nq}\times \dfrac{(n^{\frac{1}{3}}r)^2}{r^2}$

$=n^{-\frac{1}{3}}$

$=64^{-\frac{1}{3}}$

$=\dfrac{1}{4}$

hence the ratio is $1:4$

The force of attraction between two charges separated by certain distance in air is F1. If the space between the charges is completely filled with dielectric of constant 4 the force becomes F2. If half of the distance between the charges is filled with same dielectric the force between the charges is F3. Find F1:F2:F3 is

  1. 16 : 9 : 4

  2. 9 : 36 : 16

  3. 4 : 1 : 2

  4. 36 : 9 :16


Correct Option: A

Water possesses a high dielectric constant, therefore

  1. it always contains ions

  2. it is an universal solvent

  3. can dissolve covalent compounds

  4. can conduct electricity


Correct Option: A

Two charges placed at a distance experience a force of x N.The force between the charges when each charge is doubled, distance between them is halved and charge placed in a medium of dielectric constant 2.52 is.

  1. 634 X

  2. 63.4 X

  3. 40.3 X

  4. 0.403 X


Correct Option: C

Two fixed charges separated by a distance $d$ experience a force $F$. A dielectric medium of thickness $\dfrac{d}{4}$ and dielectric constant $4$ is introduced in the space between them. Find the new force between the charges.

  1. $\dfrac{F}{4}$

  2. $\dfrac{F}{3}$

  3. $F$

  4. $\dfrac{16F}{25}$


Correct Option: A
Explanation:
The force between the 2 charged particles is inversely proportional to the permittivity.

Therefore if the permittivity increases by 4 times, then obviously the force decreases by 4 times.

Therefore the new force is given by, $\dfrac{F}{4}$

The relative permittivity of water is 81. If $\varepsilon _0$ and $\varepsilon$ are permittivities of vaccum and water respectively Then:

  1. $\varepsilon _0 = 9\varepsilon _w$

  2. $\varepsilon _0= 81\varepsilon _w$

  3. $\varepsilon _w = 9\varepsilon _0$

  4. $\varepsilon _w = 81\varepsilon _0$


Correct Option: D
Explanation:

The relative permittivity of water id defined as:

$\varepsilon _{rel}=\dfrac{\varepsilon _w}{\varepsilon _0}$

Substituting the values:
$81=\dfrac{\varepsilon _w}{\varepsilon _0}$

So, $\varepsilon _w=81\ \varepsilon _0$

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${ 30 }^{ o }$ with each other. When suspended in a liquid of density $0.8g { cm }^{ -3 }$ the angle remains the same. If density of the material of the sphere is $1.6g { cm }^{ -3 }$ the dielectric constant of the liquid is:

  1. 2

  2. 1

  3. 4

  4. 3


Correct Option: A

The capacitance of an air filled parallel plate capacitor is $8 pF$. The separation between the plates is doubled and the space between the plates is then filled with wax giving the capacitance a new value of $80 \times 10^{-12}$ farads. 
The dielectric constant of wax is

  1. $5.0$

  2. $10.0$

  3. $8.0$

  4. $4.2$


Correct Option: A

The dielectric strength of air is nearly ___ V/mm

  1. 1

  2. infinite

  3. 1000

  4. 3000


Correct Option: A

What is the value of dielectric constant for metal ?

  1. zero

  2. 1

  3. infinite

  4. 2


Correct Option: B

Surface charge density of a disc is given by $\sigma = \dfrac{\sigma _o r}{R}$ where $\sigma _0$ is a constant, $r$ is distance from the center, and $R$ is the radius of the disc. If electric potential at the centre of the disc is $\dfrac{\sigma _0 R}{\alpha \epsilon _0}$ then find value of $\alpha$.

  1. $2$

  2. $1$

  3. $4$

  4. $0.5$


Correct Option: A

The ratio of the forces between two small spheres with constant charges, in air and in a medium of dielectric constant $K$, is

  1. $1:K$

  2. $K:1$

  3. $1:K^{2}$

  4. $:k{2}:1$


Correct Option: C

Two conducting spheres of radii $r _1$ and $r _2$ are charged to the same surface charge density. The ratio of electric fields near their surface is -

  1. $\dfrac { { r } _{ 1 }^{ 2 } }{ { r } _{ 2 }^{ 2 } } $

  2. $\dfrac { { r } _{ 2 }^{ 2 } }{ { r } _{ 1 }^{ 2 } } $

  3. $\dfrac{r _1}{r _2}$

  4. $1:1$


Correct Option: A

Two identical balls each having mass density $ \rho $ mass m and charge q are suspended from a common point by two insulating mass less string of equal length .At equilibrium each string makes an angle $ \theta $ with the vertical Now both the balls are immersed in a liquid.At equilibrium $ \theta $ remains same If the mass density of liquid is $ \sigma $ then dielectric constant of liquid will be

  1. $ \dfrac {\sigma}{\rho-\sigma} $

  2. $ \dfrac {\rho}{\rho-\sigma} $

  3. $ \dfrac {\sigma}{\rho} $

  4. $ \dfrac {\rho}{sigma} $


Correct Option: B

Force $'F'$ exists between two point charges in air, if a medium having $\epsilon _{R} = 6$ is inserted between charges, the new force between them.

  1. Will increase by $6$ times

  2. Will decrease by $6$ times

  3. Will decrease by $\sqrt {6}$ times

  4. Will increase by $36$ times


Correct Option: B

Two identical balls each having mass density $ \rho _1 $ mass m and charge q are suspended from a common point by two insulating massless strings of angle $\theta$ with the vertical. Now both the ball are immersed in a liquid.At equilibrium, $ \theta $ remain same. If the mass density of liquid is $ \sigma  $ then dielectric constant of liquid will be

  1. $ \frac {\sigma }{\rho - \sigma } $

  2. $ \frac {\rho }{\rho - \sigma } $

  3. $ \frac {\sigma }{\rho } $

  4. $ \frac {\rho }{ \sigma } $


Correct Option: A

Two charges when kept at a distance of $1 m$ apart in vacuum have some force of repulsion. If the force of repulsion between these two charges be same, when placed in an oil of dielectric constant $4$, the distance of separation is 

  1. $0.25m$

  2. $0.4m$

  3. $0.5m$

  4. $0.6m$


Correct Option: A

The induced charge on the dielectric of a capacitor of capacitance $4\mu F$ when charged by a battery of $50$V, is (dielectric constant of the dielectric $=4$):

  1. $100\mu C$

  2. $200\mu C$

  3. $50\mu C$

  4. $150\mu C$


Correct Option: D

When a metal plate is introduced between the two plates of a charged capacitor and insulated from them, then

  1. the metal plate divides the capacitor into two capacitors connected in parallel to each other

  2. the metal plate divides the capacitor into two capacitors connected in series with each other

  3. the metal plate is equivalent to a dielectric of zero dielectric constant

  4. the metal plate is equivalent to a dielectric of infinite dielectric constant


Correct Option: B,D
Explanation:

The capacitor is divided into two capacitors joined in series. So (b) is correct. Also as K for a metal is $\infty$, therefore (d) is also correct.

A charge is placed at some distance from a non uniform conductor . Now charge is slowly moved towards the conductor at a slow rate ,now which of the following is correct regarding it,

  1. surface charge density increases

  2. surface charge density decreases

  3. more charge is accumulated inside the conductor because of higher electric field.

  4. force is required to maintain the constant rate of movement of charge towards the conductor.


Correct Option: A,D

On the application of electric field on a dielectric and a conductor one by one which of the following is observed

  1. electric field inside the conductor is more as compared to dielectric.

  2. electric charge on the surface of conductor is more as compared to dielectric.

  3. electric potential energy entrapped in dielectric is more as compared to conductor .

  4. dielectric breakdown (if produced ) may allow the dielectric to function as a conductor with respect to flow of current.


Correct Option: B,D

Which of the following statement is correct regarding dielectric?

  1. Dielectric constant is the numerical value which signifies the extent of electric field decreased passing through it.

  2. Conductor can be considered as dielectric having dielectric constant as infinite

  3. The dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space.

  4. None of the above


Correct Option: A,B,C

Which of the material can be used as a dielectric?

  1. Ceramics

  2. Wood

  3. Copper

  4. Aluminium


Correct Option: A,B
Explanation:

we know that only non conductor can be used as a dilectric.So only A and B are correct option.

Dielectric constant, property of an electrical insulating material (a dielectric) equal to

  1. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum without the dielectric material.

  2. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum with the dielectric material.

  3. the capacitance of a capacitor filled with the given material 

  4. none  of the above 


Correct Option: A
Explanation:

The capacitance of a parallel plate capacitor filled with the given material of dielectric constant $K$ is given by:

              $C=\dfrac{K\varepsilon _{0}A}{d}$ .....................eq1
And the capacitance of the same capacitor without the given material is given by:
              $C'=\dfrac{\varepsilon _{0}A}{d}$  .....................eq2
Dividing eq1 by eq2,
              $C/C'=K$

Which of the following can be used as dielectric?

  1. Mineral oil

  2. Electrets

  3. Sulfur hexafluoride

  4. None of the above


Correct Option: A,B,C
Explanation:

We know that dielectric is a medium or substance with a dielectric property; an insulator.So, from the option Mineral oil,Electrets and also Sulfur hexafluoride can be used as dilectric.

Therefore, A,B and C are correct option.

 The capacitance of a capacitor

  1. filled with a dielectric is lesser than it would be in a vacuum.

  2. filled with a dielectric is greater than it would be in a vacuum.

  3. filled with a dielectric is same as it would be in a vacuum.

  4. none of the above 


Correct Option: B
Explanation:

The capacitance of a parallel plate capacitor filled with dielectric of dielectric constant $K$ is,

           $C=\dfrac{K\varepsilon _{o}A}{d}$  ..................eq1
and the capacitance of a parallel plate capacitor without dielectric in a vacuum is,
           $C'=\dfrac{\varepsilon _{o}A}{d}$  ...................eq2
Dividing eq1 by eq2 , we get
            $C=KC'$
as $K>1$ , therefore $C>C'$ therefore the capacitance of a capacitor filled with a dielectric is greater than it would be in a vacuum.

The voltage can be increased, but electric breakdown will occur if the electric field inside the capacitor becomes too large. The capacity can be increased by 

  1. expanding the electrode areas 

  2. reducing the gap between the electrodes

  3. expanding the gap between the electrodes

  4. Both A and B


Correct Option: D
Explanation:

The capacitance of an air filled parallel plate capacitor is given by:

            $C=\dfrac{\varepsilon _{0}A}{d}$  ..........................eq1
where $A=$ area of each plate (electrode),
            $d=$ distance between plates (electrodes)
from eq1 ,
           $C\propto A$
It is clear that capacity C can be increased by expanding the electrodes area,
and     $C\propto 1/d$ ,
hence, capacity C can be increased by reducing the gap between the electrodes.

A dielectric slab of thickness $6 cm$ is placed between the plates of a parallel plate capacitor. If the distance between plates is reduced by $4 cm$, the capacity of the capacitor remains the same. Find the dielectric constant of the medium.

  1. $2$

  2. $4$

  3. $6$

  4. $3$


Correct Option: D
Explanation:
 for a parallel plate capacitor 
             C = ε K   A / d
It is possible that we have air/vacuum and then a medium in between the parallel plates.  Initially there is a medium of dielectric constant K and of thickness d.

    Let  K1 be the dielectric constant of the slab.  
     let d1 be the thickness of slab = 6cm.

Formula for capacity with multiple media in between the plates is 
             C =  ε A / [ d1/K1 + d2 / K ]
          total gap =  d1 + d2 = d + 4 cm          =>  d2 = d + 4 cm - 6 cm = d - 2
 
         d / K =  d1/ K1 + d2 / K 
         d/ K = 6 / K1  + (d-2)/K

          d - (d-2)  = 6 K / K1 
                K1 = 3 K
  If there was air originally in between the plates,  K = 1,  then answer is 3.

A parallel plate condenser is charged to $100$ volt. In this context which one of the following statements is true?

  1. The two plates attract each other

  2. There is to force between the plates

  3. The two plates of the condenser repel each other

  4. The force between the plates can be attractive or repulsive depending upon the nature of the dielectric material between the plates


Correct Option: D

At room temperature, if the relative permittivity of water be $80$ and the relative permeability be $0.0222$, then the velocity of light in water is ________ $m/{s}^{-1}$

  1. $3\times { 10 }^{ 8 }\quad $

  2. $2.25\times { 10 }^{ 8 }$

  3. $2.5\times { 10 }^{ 8 }$

  4. $3.5\times { 10 }^{ 8 }$


Correct Option: B
Explanation:

Formula 

$V=\cfrac{1}{\sqrt{\mu _0\epsilon _0}}\V^1=\cfrac{1}{\mu _r\epsilon _r}\ \Rightarrow \cfrac{V}{V^1}=\sqrt{\cfrac{\mu _r\epsilon _r}{\mu _0\epsilon _0}}$
$\Rightarrow\cfrac{V^1}{V}=\sqrt{\cfrac{\mu _0}{}{\mu _r}\times\cfrac{\epsilon _0}{\epsilon _r}}=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.0222}}\ \Rightarrow V^1=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.0222}}\times V\ \quad=\sqrt{\cfrac{1}{80}\times\cfrac{1}{0.022}}\times3\times10^8\ \quad=2.249\times 10^8\ \quad\approx2.22\times10^8m/s$

Surface charge density of a thin disc having radius $R$ varies with distance from centre as $\sigma =\sigma _{0}\dfrac {R}{r}(r\neq 0) $ then total charge of disc is

  1. $2\pi \sigma _{0}R^{3}$

  2. $\sqrt {2}\pi \sigma _{0}R^{2}$

  3. $2\sqrt {2}\pi \sigma _{0}R^{2}$

  4. $2\pi \sigma _{0}R^{2}$


Correct Option: A
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