Home
Class 12
PHYSICS
Proj.j. Prakash asked Vijit whether the ...

Proj.j. Prakash asked Vijit whether the average energy density of the electric field and magnetic field are equal or not ? Viji said ''yes''. Justify the answer.

Text Solution

Verified by Experts

Velocity, `c=(1)/(sqrt(mu_(0)epsilon_(0)))` and `B_(0)=(E_(0))/(c )`
Amplitude of oscillating electric field `= E_(0)`
Amplitude of oscillating magnetic field `= B_(0)`
Average energy density in E field `= (1)/(2)epsilon_(0)E_(0)^(2)`
Average energy density in B field `= (1)/(2mu_(0))B_(0)^(2)`
`((1)/(2mu_(0)))B_(0)^(2)=(1)/(2mu_(0))(E_(0)^(2))/(c^(2))=((1)/(2mu_(0)))mu_(0)epsilon_(0)E^(2)=(1)/(2)epsilon_(0)E^(2)`
`therefore V_(B)=V_(E )`
Hence the proof.
Promotional Banner

Topper's Solved these Questions

  • ELECTROMAGNETIC WAVES

    NEW JOYTHI PUBLICATION|Exercise CONTINUOUS EVALUATION (ASSIGNMENT)|5 Videos

  • ELECTROMAGNETIC WAVES

    NEW JOYTHI PUBLICATION|Exercise PREVIOUS YEAR QUESTIONS|2 Videos

  • ELECTROMAGNETIC WAVES

    NEW JOYTHI PUBLICATION|Exercise PRACTICE PROBLEMS FOR SELF ASSESSMENT|7 Videos

  • ELECTROMAGNETIC INDUCTION

    NEW JOYTHI PUBLICATION|Exercise COMPETITIVE EXAM CORNER|13 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    NEW JOYTHI PUBLICATION|Exercise Competitive Exam Corner|22 Videos

Similar Questions

Explore conceptually related problems

The energy density in the electric field created by a point charge falls off with the distance from the point charge as

In a plane Electromagnetic wave the electric field oscillates sinusoidally at a frequency of 2.0 X 10^(10) Hz & amplitude 48 Vm^(-1) . show that the average energy density of the electric field (vec(E )) , is equal to average energy density of the magnetic field (vec(B))

Consider the following two statements regarding a linearly polarized, plane electromagnetic wave: The electric field and the magnetic field have equal average values. The electric energy and the magnetic energy have equal average values.

In a plane electromagnetic wave, the electric field oscillates sin usoidally at a frequency of 2.0xx10^(10) Hz and amplitude 48 V m^(-1) . a. What is the wavelength of the wave ? b. What is the amplitude of the oscillating magnetic field ? c. Show that the average energy density of the E field equals the average energy density of the B field. [c=3xx10^(8)ms^(-1)] .

A currrent I is passed through a silver strip of width d and area of cross section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region as shown in what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will be the potential diference developed across the width of the conductor due to the electron- accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called hall effect.

A plane electromagnetic wave is passing through a region. Consider the quantities (a) electric field, (b) magnetic field , (c) electrical energy in a small volume and (d) magnetic energy in a small volume. Construct pairs of the quantities that oscillate with equal frequencies.

A circular coil with cross - sectional area 0.1 cm^(2) is kept in a uniform magnetic field of strength 0.2 T. If the current passing in the coil is 3 A and plane of the loop is perpendicular to the direction of magnetic field . Calculate (a) total torque on the coil (b) total force on the coil (c ) average force on each electron in the coil due to the magnetic field of the free electron density for the material of the wire is 10^(28) m^(-3) .

A metal sphere of radius R is charged to a pontital V . (a ) Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R . (b )Show that the electrostatic field energy stored outside the sphere of radius 2R equals that stored within it .