# show that the average energy density of the electric field equals the average energy density of the magnetic field.

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## In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10^10 Hz and amplitude 48 V m^

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(iii) Show that the average energy density of the E field equals the average energy density of the B field. 10

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Updated on : 2022-09-05

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## Show that the average energy density of the $E$ field equals the average energy density of the $B$ field.

Show that the average energy density of the $E$ field equals the average energy density of the $B$ field.. Ans: Hint: The ratio of the amount of electric charge deposited on a conductor to the difference in electric potential is known as capacitance....

Show that the average energy density of theE E

field equals the average energy density of the

B B field.

Last updated date: 13th Mar 2023

• Total views: 200.7k • Views today: 3.80k Answer Verified 200.7k+ views

**Hint:**The ratio of the amount of electric charge deposited on a conductor to the difference in electric potential is known as capacitance. Self capacitance and reciprocal capacitance are two closely related concepts of capacitance. Self capacitance is a property of any material that can be electrically charged.

**Complete step by step answer:**

The sum of energy contained in a given structure or area of space per unit volume is referred to as energy density in physics. It may also refer to energy per unit mass, but real energy is a more precise expression (or gravimetric energy density). The cumulative sum of energy in a device per unit volume is known as energy density.

The amount of g g

of sugar in food, for example. Low energy dense foods have less calories per gram of food, allowing you to consume more of them so there are less calories. The letter

U U

is used to represent it. Magnetic and electric fields have the ability to accumulate energy as well.

As it comes to electromagnetic waves, both the magnetic and electric fields play a role in determining energy density. As a result, the expression for energy density is the sum of the electric and magnetic field's energy density. For average magnetic density we have

Since, U B = 1 2 μ 0 B 2 UB=12μ0B2

For average energy density, we have

U E = 1 2 ε 0 E 0 2 UE=12ε0E02 ⇒ E 0 B 0 =C ⇒E0B0=C

On substitution we have

U E = 1 4 ε 0 ⋅ C 2 B 0 2 UE=14ε0⋅C2B02

We know that the speed of Electromagnetic waves is

C= 1 μ 0 E 0 − − − − √ C=1μ0E0

Upon substitution we get,

U E = 1 4 ε 0 B 2 0 ⋅ 1 μ 0 ε 0 UE=14ε0B02⋅1μ0ε0 ⇒ U E = 1 4 B 2 O μ 0 ∴ U E =( B o 2 2 μ 0 )= U B

⇒UE=14BO2μ0∴UE=(Bo22μ0)=UB

**Hence, the average energy density of the E field equals the average energy density of the B field.**

**Note:**Electromagnetic waves, or EM waves, are waves that are produced when an electric field and a magnetic field vibrate together. EM waves, in other words, are made up of oscillating magnetic and electric fields. Electromagnetic radiation is a term used in physics to describe the waves of the electromagnetic field that propagate through space and carry electromagnetic radiant energy. Radio waves, microwaves, infrared, sun, ultraviolet, X-rays, and gamma rays are also examples of electromagnetic radiation. The electromagnetic spectrum includes both of these waves.

## Show that the avearge energy density of the electric field vecE equals the average energy density of the magnetic field vecB, in electromagnetic waves.

Average energy density of E U(E) = (1)/(4) epsilon(0) E(0)^(2) Average energy density of B U(B) = (1)/(4) (B(0)^(2))/(mu(0)) because c = (E0)/(B0) So. U(E) = (1)/(4) epsilon(0) (c B(0))^(2) = (1)/(4) epsilon(0) c^(2) B(0)^(2) = (1)/(4) epsilon(0) (1)/((mu(0) epsilon(0))) xx B(0)^(2) = (1)/(4) (B(0)^(2))/(mu(0)) U(E) = U(B)

Show that the avearge energy density of the electric field

→ E

equals the average energy density of the magnetic field

→ B

, in electromagnetic waves.

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AAKASH INSTITUTE ENGLISH-ELECTROMAGNETIC WAVES-ASSIGNMENT SECTION - D ASSERTION-REASON TYPE QUESTIONS

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Hello today we have question so that the average energy density of the electric field equals the average energy density of the magnetic field in electromagnetic that the average energy density in electric field is given by 1 by 4 in not expire ok hair apply not electric community and the Knot is maximum value of electric field also be not there them average energy density of magnetic field is given by 1 by 4 be not a square new note and be noticed the maximum value of magnetic field

you also know electromagnetic wave the ratio of in note to be not is given by electromagnetic waves this value in this situation you will get their value in what will be seen to be not do in this situation h u become 14 CBD note we will get 1 by 4 notes Vinod square so also be noted that in the electromagnetic new note and excellent value in it will become 1

by 4 one upon under root Mu not as line not a square B not square we will get you equal to 1 by 4 into one upon us not into we not a square not 1.4 be not a square upon x is equal to you become equals to give we have to prove so we can say average density of electric field is equal to average energy density of magnetic field

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Show that the average energy density of the electric field vecE equals the average energy density of the magnetic field vecB , in electromagnetic waves.

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Show that the avearge energy density of the electric field

→ E

equals the average energy density of the magnetic field

→ B

, in electromagnetic waves.

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Show that the avearge energy density of the electric field

→ E

equals the average energy density of the magnetic field

→ B

, in electromagnetic waves.

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In a plane electomagnetic wave, the electric field oscillates sinusoidally at a frequency of

2.0 × 106 ( 10 ) H z and amplitude 48 V m − 1 .

(a) What is the wavelength of the wave?

(b) What is the amplitude of the ocillating magnetic field ?

(c ) Show that the average energy density of the

→ E

field equals the average energy density of the

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