Tag: electrostatic potential and capacitance

Questions Related to electrostatic potential and capacitance

The ratio of the forces between two small spheres with constant charges, in air and in a medium of dielectric constant $K$, is

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

  1. $1:K$

  2. $K:1$

  3. $1:K^{2}$

  4. $:k{2}:1$

Show answer
Correct Option: C

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 -

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

  1. $\dfrac { { r } _{ 1 }^{ 2 } }{ { r } _{ 2 }^{ 2 } } $

  2. $\dfrac { { r } _{ 2 }^{ 2 } }{ { r } _{ 1 }^{ 2 } } $

  3. $\dfrac{r _1}{r _2}$

  4. $1:1$

Show answer
Correct Option: A

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

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

  1. $ \dfrac {\sigma}{\rho-\sigma} $

  2. $ \dfrac {\rho}{\rho-\sigma} $

  3. $ \dfrac {\sigma}{\rho} $

  4. $ \dfrac {\rho}{sigma} $

Show answer
Correct Option: B

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.

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

  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

Show answer
Correct Option: B

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

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

  1. $ \frac {\sigma }{\rho - \sigma } $

  2. $ \frac {\rho }{\rho - \sigma } $

  3. $ \frac {\sigma }{\rho } $

  4. $ \frac {\rho }{ \sigma } $

Show answer
Correct Option: A

Two charges when kept at a distance of $1 m$ apart in vacuum have some force of repulsion. If the force of repulsion between these two charges be same, when placed in an oil of dielectric constant $4$, the distance of separation is 

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

  1. $0.25m$

  2. $0.4m$

  3. $0.5m$

  4. $0.6m$

Show answer
Correct Option: A

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 $=4$):

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

  1. $100\mu C$

  2. $200\mu C$

  3. $50\mu C$

  4. $150\mu C$

Show answer
Correct Option: D

When a metal plate is introduced between the two plates of a charged capacitor and insulated from them, then

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

  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

Show answer
Correct Option: B,D
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.

A charge is placed at some distance from a non uniform conductor . Now charge is slowly moved towards the conductor at a slow rate ,now which of the following is correct regarding it,

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

  1. surface charge density increases

  2. surface charge density decreases

  3. more charge is accumulated inside the conductor because of higher electric field.

  4. force is required to maintain the constant rate of movement of charge towards the conductor.

Show answer
Correct Option: A,D

On the application of electric field on a dielectric and a conductor one by one which of the following is observed

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

  1. electric field inside the conductor is more as compared to dielectric.

  2. electric charge on the surface of conductor is more as compared to dielectric.

  3. electric potential energy entrapped in dielectric is more as compared to conductor .

  4. dielectric breakdown (if produced ) may allow the dielectric to function as a conductor with respect to flow of current.

Show answer
Correct Option: B,D