Tag: electrostatic potential and capacitance

Questions Related to electrostatic potential and capacitance

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

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. greater than 1

  2. equal to 1

  3. lesser than 1 

  4. None 

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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

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  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

Show answer
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?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. Silicon dioxide

  2. Silicon nitride 

  3. Titanium oxide

  4. None of the above

Show answer
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.

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. True

  2. False

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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

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

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

Show answer
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:

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. 2.4

  2. 5.8

  3. 8.2

  4. 4.8

Show answer
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

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $2.6$

  2. $3$

  3. $4$

  4. $5$

Show answer
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: 

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $2.5$

  2. $0.25$

  3. $2.0$

  4. $4.0$

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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 ?

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  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

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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:

dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

  1. $4:1$

  2. $1:4$

  3. $1:64$

  4. $64:1$

Show answer
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 $1:4$