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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
A Correct answer
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.

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

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 } $
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

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. $150\mu C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Induced charge Q_i = Q_free * (1 - 1/K). Q_free = C_air * V = 4uF * 50V = 200uC. Q_i = 200 * (1 - 1/4) = 200 * 0.75 = 150uC.

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

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
Reveal answer Fill a bubble to check yourself
B,D Correct answer
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.