Tag: electrostatics

Quizzes (15) Questions (156)

Questions Related to electrostatics

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.

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

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. $:k{2}:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The electrostatic force between charges in a medium is inversely proportional to the dielectric constant K of the medium. The ratio of the force in air to the force in the medium is therefore K:1.

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

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. $1:1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The electric field near the surface of a charged conducting sphere is given by E = sigma / epsilon_0, where sigma is the surface charge density. Since the spheres are charged to the same surface charge density, the electric fields near their surfaces are equal, yielding a ratio of 1:1.

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

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} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the equilibrium condition for suspended charges in a medium: K = rho / (rho - sigma).

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

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

The force in a medium is F_medium = F_air / K. With K=6, the force decreases by 6 times.