Prove that total electrostatic potential energy stored in a capacitor is 1 2 CV 2 . Hence, derive an expression for the energy density of an electric field.

Expression for the stored energy- Suppose a parallel plate capacitor has capacitance.On plats charges are + q and - q and their potential differences is V . ∴ V = q / C . . . . . . . . . . . . ( i ) Now d q charge is transferred than work done. d w = v d q = q / C d q from(i) Now work done in transferring total Q charge. This work is stored in capacitor as potential energy ( U ) . Expression for energy density-

MEDIUM

Earn 100

In a parallel plate capacitor, the distance between the plates is $d$ and potential difference across the plates is $V$ . Energy stored per unit volume between the plates of capacitor is

80% studentsanswered this correctly

Important Questions on Electrostatic Potential and Capacitance

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

What is the potential energy of a capacitor? Derive its expression. Where and in which form this energy is found?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

A $600 μF$ capacitor is charged by a $200 V$ supply. It is then disconnected from the supply and is connected to another uncharged $600 μF$ capacitor. How much electrostatic energy is lost in the process?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Derive an expression for energy stored in a charged capacitor.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Obtain the expression for the energy stored in a parallel plate capacitor of capacitance

C

charged to a potential

V

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

The electric field in an electromagnetic wave is given by

E = (50 N C^{- 1}) \sin ω (t - \frac{x}{c})

The energy contained in a cylinder of volume

V

5.5 \times 10^{- 12} J .

The value of

V

is _______

{cm}^{3} .

(given

ϵ_{0} = 8.8 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}

)

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Prove that total electrostatic potential energy stored in a capacitor is

\frac{1}{2} {CV}^{2}

. Hence, derive an expression for the energy density of an electric field.

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

700 pF

capacitor is charged by a

50 V

battery. How much electrostatic energy is stored by it?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

A $600 pF$ capacitor is charged by a $200 V$ supply. It is then disconnected from the supply and is connected to another uncharged $600 pF$ capacitor. How much electrostatic energy is lost in the process?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Write the expression for energy stored in a capacitor in terms of capacitance and potential difference between its plates.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

The energy per unit volume for a capacitor having area

A

and separation

d

kept at potential difference

V

is given by

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

How does the magnetic energy stored in an inductor and electrostatic energy stored in a capacitor related to their respective field strengths?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

What does mean by energy stored in capacitor?

Prove that-

"The ratio of change in potentials of conductors after connecting two charged conductors in inversely proportional to their capacitances".

Draw a curve between electric field and distance for an uniformly charged non-conducting sphere.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

On increasing the potential difference of a

8

micro-farad capacitor from

20

volt to

25

volt, calculate the increase in its potential energy.

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Derive the expression for the energy stored in a charged capacitor.

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Derive an expression for the energy stored in a capacitor. In what form is the energy stored in a charged capacitor?

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

In figure, charge on the capacitor is plotted against potential difference across the capacitor. The capacitance and energy stored in the capacitor are respectively.

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Energy Density in Electric Field

A parallel plate capacitor has a uniform electric field

\vec{E}

in the space between the plates. If the distance between the plates is

d

and the area of each plate is

A

, the energy stored in the capacitor is:

ε_{0} =

permittivity of free space)

In a parallel plate capacitor, the distance between the plates is d and potential difference across the plates is V. Energy stored per unit volume between the plates of capacitor is

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

In a parallel plate capacitor, the distance between the plates is $d$ and potential difference across the plates is $V$ . Energy stored per unit volume between the plates of capacitor is