Answer
385.8k+ views
Hint:The total number of magnetic lines of force passing normally through an area placed in a magnetic field is equal to the magnetic flux linked with that area. The process by which an emf is induced in a circuit by the virtue of changing the magnetic field around it is known as electromagnetic induction.
Complete step by step answer:
Magnetic Field$\left( B \right)$: A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. This magnetic field can be seen as imaginary lines known as the magnetic field lines.
Magnetic Flux $\left( \varphi \right)$: The total number of magnetic lines of force passing normally through an area$\left( A \right)$ placed in a magnetic field$\left( B \right)$ is equal to the magnetic flux linked with that area. That is,
$\varphi = \oint {\overrightarrow B .d\overrightarrow A } $
The SI unit of magnetic flux is weber$\left( {Wb} \right)$.
Faraday’s Laws of Electromagnetic Induction:
First Law: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes, an emf called induced emf is produced in the circuit. The induced emf persists as long as there is change of flux.
Second Law: The induced emf $\left( \varepsilon \right)$ is given by the rate of change of magnetic flux linked with the circuit. That is,
$\varepsilon = - \dfrac{{d\varphi }}{{dt}}$
For $N$ turns, $\varepsilon = - \dfrac{{Nd\varphi }}{{dt}}$.
So, in the above case,
$\varepsilon = - \dfrac{{50 \times d\left( {0.02\cos 100\pi t} \right)}}{{dt}}$
$ \Rightarrow \varepsilon = - 50 \times \left( {0.02} \right) \times \left\{ { - \sin 100\pi t} \right\} \times 100\pi $
$ \Rightarrow \varepsilon = 100\pi \sin 100\pi t$
For maximum emf, $\sin 100\pi t = 1$. So,
$ \Rightarrow \varepsilon = 100 \times 3.14$
$\therefore \varepsilon = 314volt$
Thus, the correct answer is option A.
Note:Since magnetic flux is the dot product of magnetic field vector and areal vector, therefore magnetic flux is a scalar quantity. As soon as the magnetic flux stops changing the induced emf returns to zero.
Complete step by step answer:
Magnetic Field$\left( B \right)$: A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. This magnetic field can be seen as imaginary lines known as the magnetic field lines.
Magnetic Flux $\left( \varphi \right)$: The total number of magnetic lines of force passing normally through an area$\left( A \right)$ placed in a magnetic field$\left( B \right)$ is equal to the magnetic flux linked with that area. That is,
$\varphi = \oint {\overrightarrow B .d\overrightarrow A } $
The SI unit of magnetic flux is weber$\left( {Wb} \right)$.
Faraday’s Laws of Electromagnetic Induction:
First Law: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes, an emf called induced emf is produced in the circuit. The induced emf persists as long as there is change of flux.
Second Law: The induced emf $\left( \varepsilon \right)$ is given by the rate of change of magnetic flux linked with the circuit. That is,
$\varepsilon = - \dfrac{{d\varphi }}{{dt}}$
For $N$ turns, $\varepsilon = - \dfrac{{Nd\varphi }}{{dt}}$.
So, in the above case,
$\varepsilon = - \dfrac{{50 \times d\left( {0.02\cos 100\pi t} \right)}}{{dt}}$
$ \Rightarrow \varepsilon = - 50 \times \left( {0.02} \right) \times \left\{ { - \sin 100\pi t} \right\} \times 100\pi $
$ \Rightarrow \varepsilon = 100\pi \sin 100\pi t$
For maximum emf, $\sin 100\pi t = 1$. So,
$ \Rightarrow \varepsilon = 100 \times 3.14$
$\therefore \varepsilon = 314volt$
Thus, the correct answer is option A.
Note:Since magnetic flux is the dot product of magnetic field vector and areal vector, therefore magnetic flux is a scalar quantity. As soon as the magnetic flux stops changing the induced emf returns to zero.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)