Tag: electrostatics

Questions Related to electrostatics

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

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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 $1:4$

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

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

  1. 16 : 9 : 4

  2. 9 : 36 : 16

  3. 4 : 1 : 2

  4. 36 : 9 :16

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Correct Option: A

Water possesses a high dielectric constant, therefore

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

  1. it always contains ions

  2. it is an universal solvent

  3. can dissolve covalent compounds

  4. can conduct electricity

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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.

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

  1. 634 X

  2. 63.4 X

  3. 40.3 X

  4. 0.403 X

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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.

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

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

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

  3. $F$

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

Show answer
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, $\dfrac{F}{4}$