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Two conducting square plates with length $l$ are arranged parallel to each other at a distance $d (≪ 1)$ . The space between the plates is filled with a dielectric of relative permittivity $ε_{r} = 4$ up to a length $x = l / 3$ . The upper plate is given a charge $Q$ and the lower plate is given a charge $- Q$ as shown in the figure. If $Q = 6 μ C$ then find how much charge (in $μ C$ ) is present on the portion of upper plate which is in contact with the dielectric?

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Important Questions on Electrostatic Potential and Capacitance

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

Three identical capacitors

C_{1}, C_{2} a n d C_{3}

have a capacitance of

1.0 μ F

each and they are uncharged initially. They are connected in a circuit as shown in the figure and

C_{1}

is then filled completely with a dielectric material of relative permittivity

ϵ_{r}

. The cell electromotive force (emf)

V_{0} = 8 V

. First the switch

S_{1}

is closed while the switch

S_{2}

is kept open. When the capacitor

C_{3}

is fully charged,

S_{1}

is opened and

S_{2}

is closed simultaneously. When all the capacitors reach equilibrium, the charge on

C_{3}

is found to be

5 μ C

. The value of

ϵ_{r}

=____________.

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EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

The capacitance of a parallel plate capacitor with air as medium is

6 μ F

. With the introduction of a dielectric medium, the capacitance becomes

30 μ F

. The permittivity of the medium is:

(ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plate capacitor with air between the plates has a capacitance of

9 pF

. The separation between the plates is

d

. The space between the plates is now filled with two dielectrics constant

K_{1} = 3

and thickness

\frac{d}{3}

while the other one has dielectric constant

K_{2} = 6

and thickness

\frac{2 d}{3}

. Capacitance of the capacitor is now

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_{1}, K_{2}, K_{3}, K_{4}$ arranged as shown in the figure. The effective dielectric constant $K$ will be:

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MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

Voltage rating of a parallel plate capacitor is

500 V .

Its dielectric can withstand a maximum electric field of

10^{6} V m^{- 1} .

The plate area is

10^{- 4} m^{2}

. What is the dielectric constant if the capacitance is

15 p F

(given ϵ_{0} = 8.86 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

An uncharged parallel plate capacitor filled with an oil is connected in parallel with an identical but air filled capacitor charged to a potential

V_{1}

. If the common potential is

V_{2}

, the dielectric constant of the oil is

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel-plate capacitor of area $A$ , plate separation $d$ and capacitance $C$ is filled with four dielectric materials having dielectric constants $k_{1}$ , $k_{2}$ , $k_{3}$ and $k_{4}$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by

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EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plate capacitor has a capacity

C .

The separation between the plates is doubled and a dielectric medium is inserted between the plates. If the capacity is

3 C,

then the dielectric constant of the medium will be

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

Two identical parallel plate capacitors, of capacitance

C

each, have plates of area

A,

separated by a distance

d

. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants

K_{1}, K_{2}

and

K_{3}

. The first capacitor is filled as shown in figure

I,

and the second one is filled as shown in figure

I I .

If these two modified capacitors are charged by the same potential

V

, the ratio of the energy stored in the two, would be

(E_{1}

refers to capacitor

(I)

and

E_{2}

to capacitor

(I I)

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

Two thin dielectric slabs of dielectric constants

K_{1}

and

K_{2} (K_{1} < K_{2})

are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field ‘

E

’ between the plates with distance ‘

d

’ as measured from plate

P

is correctly shown by:
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HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching each other due to electrostatic attraction. Assuming no other force to be operative and no radiation taking place, which of the following graphs approximately shows the variation with time

(t)

of the potential difference

(V)

between the plates?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

Two parallel plate air capacitors of the same capacity

C

are connected in series to a battery of emf

E

. Then one of the capacitors is completely filled with the dielectric material of constant

K

. The change in the effective capacitance of the series combination is

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A capacitor is kept connected to a battery and a dielectric slab is inserted between the plates. During the process

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

The capacitance of a parallel plate capacitor becomes

\frac{4}{3}

times its original value if a dielectric slab of thickness

t = \frac{d}{2}

is inserted between the plates (where

d

is the distance of separation between the plates). What is the dielectric constant of the slab?

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

The region between the parallel plates of a capacitor is filled with parallel layers of air and paper (of dielectric constant

4

). The space between the plates is

1 mm

and the thickness of paper is

0.75 mm .

The ratio of the voltages across air and paper is

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A simple pendulum of mass ' $m$ ', length ' $l$ ' and charge $' + q^{'}$ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

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MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plated capacitor has area

2 m^{2}

separated by

3

dielectric slabs. Their relative permittivity is

2, 3, 6

and thickness is

0.4 mm, 0.6 mm, 1.2 mm

respectively. The capacitance is

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A capacitance of a parallel plate air capacitor is

10 μF .

Dielectric constant of the medium to be introduced in between its plates to double its capacitance is

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plate capacitor of capacitance

90 pF

is connected to a battery of EMF

20 V

. If a dielectric material of dielectric constant

K = \frac{5}{3}

is inserted between the plates, the magnitude of the induced charge will be:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Effect of Dielectric on Capacitance

A parallel plate air capacitor has capacity

C

, distance of separation between plates is

d

and potential difference

V

is applied between the plates. The force of attraction between the plates of the capacitor is

Important Questions on Electrostatic Potential and Capacitance

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