Tag: dielectric substances and polarization

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Questions Related to dielectric substances and polarization

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

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. $\dfrac{16F}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $\dfrac{F}{4}$
Multiple choice dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

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. $\varepsilon _w = 81\varepsilon _0$
Reveal answer Fill a bubble to check yourself
D Correct answer
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, $\varepsilon _w=81\ \varepsilon _0$

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equilibrium in air: tan(theta) = F_e / (mg). In liquid: tan(theta) = F_e' / (mg - F_buoyant). Since theta is same, F_e/mg = F_e'/(mg - F_b). Substituting F_e' = F_e/K and F_b = V*sigma*g, we get K = rho / (rho - sigma) = 1.6 / (1.6 - 0.8) = 1.6 / 0.8 = 2.

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

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. $4.2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

C_air = epsilon_0 * A / d = 8 pF. C_wax = K * epsilon_0 * A / (d/2) = 2 * K * C_air = 80 pF. Thus 2 * K * 8 = 80, so K = 5.

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

What is the value of dielectric constant for metal ?

  1. zero

  2. 1

  3. infinite

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The dielectric constant of a metal is effectively 1 because metals are perfect conductors. In an ideal conductor, the electric field inside is zero in electrostatic conditions, and the polarization response is such that εr = 1. This is because free electrons can move instantly to cancel any internal field. The apparent 'infinite' capacitance in parallel plate capacitors comes from geometry, not material properties.

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

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. $0.5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Integrating the potential contribution from concentric ring elements of charge dq over the disc yields the electric potential at the center. Solving the integration with the given surface charge density results in alpha equal to 4.