Answer
Verified
386.3k+ views
Hint: The expression of the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid can be given using the following formulas which are as follows:
\[{{\varepsilon }_{\circ }}=\dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\]
\[E=Bc\]
\[\dfrac{U}{Al}=\dfrac{1}{2}\times {{\varepsilon }_{\circ }}\times {{E}^{2}}\]
Complete step-by-step answer:
The permittivity of a particular medium is given by,
\[{{\varepsilon }_{\circ }}=\dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\] …(1)
Now, the electric field generated by a magnetic field of strength B is given by,
\[E=Bc\] ….(2)
The value of the energy stored in a capacitor for per volume is given as follows,
\[\dfrac{U}{Al}=\dfrac{1}{2}\times {{\varepsilon }_{\circ }}\times {{E}^{2}}\]
Substituting values from equation (1) and equation (2) we get,
\[U=\dfrac{1}{2}\times \dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\times {{\left( Bc \right)}^{2}}\times Al\]
\[U=\dfrac{1}{2}\times \dfrac{1}{{{\mu }_{\circ }}}\times {{B}^{2}}\times Al\]
Therefore, the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid is \[\dfrac{1}{2}\dfrac{{{B}^{2}}}{{{\mu }_{\circ }}}\times Al\] which is the correct answer.
Note: A solenoid is a type of electromagnet which has a purpose of generating a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged in a given manner to produce a uniform magnetic field in a volume of space when an electric current is passed through it. The solenoid works on the principle of electromagnetism. When the current flow through the coil magnetic field is generated in it and then if you place a metal core inside the coil the magnetic lines of flux are concentrated on the core which increases the induction of the coil as compared to the air core.
\[{{\varepsilon }_{\circ }}=\dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\]
\[E=Bc\]
\[\dfrac{U}{Al}=\dfrac{1}{2}\times {{\varepsilon }_{\circ }}\times {{E}^{2}}\]
Complete step-by-step answer:
The permittivity of a particular medium is given by,
\[{{\varepsilon }_{\circ }}=\dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\] …(1)
Now, the electric field generated by a magnetic field of strength B is given by,
\[E=Bc\] ….(2)
The value of the energy stored in a capacitor for per volume is given as follows,
\[\dfrac{U}{Al}=\dfrac{1}{2}\times {{\varepsilon }_{\circ }}\times {{E}^{2}}\]
Substituting values from equation (1) and equation (2) we get,
\[U=\dfrac{1}{2}\times \dfrac{1}{{{c}^{2}}{{\mu }_{\circ }}}\times {{\left( Bc \right)}^{2}}\times Al\]
\[U=\dfrac{1}{2}\times \dfrac{1}{{{\mu }_{\circ }}}\times {{B}^{2}}\times Al\]
Therefore, the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid is \[\dfrac{1}{2}\dfrac{{{B}^{2}}}{{{\mu }_{\circ }}}\times Al\] which is the correct answer.
Note: A solenoid is a type of electromagnet which has a purpose of generating a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged in a given manner to produce a uniform magnetic field in a volume of space when an electric current is passed through it. The solenoid works on the principle of electromagnetism. When the current flow through the coil magnetic field is generated in it and then if you place a metal core inside the coil the magnetic lines of flux are concentrated on the core which increases the induction of the coil as compared to the air core.
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
Which are the Top 10 Largest Countries of the World?
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
How do you graph the function fx 4x class 9 maths CBSE
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
What organs are located on the left side of your body class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell