Answer
Verified
375.9k+ 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 $g$ 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 $U$ 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, ${U_B} = \dfrac{1}{{2{\mu _0}}}{B^2}$
For average energy density, we have
${{\text{U}}_{\text{E}}} = \dfrac{1}{2}{\varepsilon _0}{{\text{E}}_0}^2$
$\Rightarrow \dfrac{{{E_0}}}{{{B_0}}} = C$
On substitution we have
${{\text{U}}_{\text{E}}} = \dfrac{1}{4}{\varepsilon _0} \cdot {{\text{C}}^2}\;{{\text{B}}_0}^2$
We know that the speed of Electromagnetic waves is
${\text{C}} = \dfrac{1}{{\sqrt {{\mu _0}{{\text{E}}_0}} }}$
Upon substitution we get,
${{\text{U}}_{\text{E}}} = \dfrac{1}{4}{\varepsilon _0}\;{\text{B}}_0^2 \cdot \dfrac{1}{{{\mu _0}{\varepsilon _0}}}$
$\Rightarrow {{\text{U}}_{\text{E}}} = \dfrac{1}{4}\dfrac{{{\text{B}}_{\text{O}}^2}}{{{\mu _0}}} \\
\therefore {{\text{U}}_{\text{E}}}= \left( {\dfrac{{{{\text{B}}_o}^2}}{{2{\mu _0}}}} \right) = {U_{\text{B}}}$
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.
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 $g$ 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 $U$ 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, ${U_B} = \dfrac{1}{{2{\mu _0}}}{B^2}$
For average energy density, we have
${{\text{U}}_{\text{E}}} = \dfrac{1}{2}{\varepsilon _0}{{\text{E}}_0}^2$
$\Rightarrow \dfrac{{{E_0}}}{{{B_0}}} = C$
On substitution we have
${{\text{U}}_{\text{E}}} = \dfrac{1}{4}{\varepsilon _0} \cdot {{\text{C}}^2}\;{{\text{B}}_0}^2$
We know that the speed of Electromagnetic waves is
${\text{C}} = \dfrac{1}{{\sqrt {{\mu _0}{{\text{E}}_0}} }}$
Upon substitution we get,
${{\text{U}}_{\text{E}}} = \dfrac{1}{4}{\varepsilon _0}\;{\text{B}}_0^2 \cdot \dfrac{1}{{{\mu _0}{\varepsilon _0}}}$
$\Rightarrow {{\text{U}}_{\text{E}}} = \dfrac{1}{4}\dfrac{{{\text{B}}_{\text{O}}^2}}{{{\mu _0}}} \\
\therefore {{\text{U}}_{\text{E}}}= \left( {\dfrac{{{{\text{B}}_o}^2}}{{2{\mu _0}}}} \right) = {U_{\text{B}}}$
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE