Answer
414.9k+ views
Hint:Here metal rod of length l, is in motion in the area where there is a magnetic field present. We know from Maxwell equations that a changing magnetic field can induce current whose direction is given by Lenz law. Also, if the magnetic flux remains constant then there will be no induced emf.
Complete step by step answer:
From the concept of motional emf, the emf induced in a conductor which is moving in the region where the magnetic field is present. So, let us find the magnetic flux,
\[\Rightarrow {{\phi }_{B}}=\overrightarrow{B.}\overrightarrow{A}=BA\cos \varphi \]
The area which the conductor covers can be written as the product of velocity and length, so, the equation becomes
\[\Rightarrow e=Blv\cos \phi \]
But we are interested in finding out the rate at which the electrical energy converted into thermal energy in the resistance of the bar after the terminal velocity has been reached.
So, we need to find the rate of generation of thermal energy.
Using the formula,
\[\Rightarrow P=\dfrac{{{V}^{2}}}{R}\] where V is the emf generated and R is the resistance of the conductor.
\[\therefore P=\dfrac{{{B}^{2}}{{l}^{2}}{{v}^{2}}{{\cos }^{2}}\phi }{R}\]
So, the correct option is (B).
Note: If there was no change in the magnetic flux then there would have been no emf induced in the conductor. Since flux is the dot product of magnetic field and area vector, to change the flux there can be three conditions:
- Change in a magnetic field.
-Change in the area of the conductor.
-Change in the angle between the magnetic field and the area vector.
Complete step by step answer:
From the concept of motional emf, the emf induced in a conductor which is moving in the region where the magnetic field is present. So, let us find the magnetic flux,
\[\Rightarrow {{\phi }_{B}}=\overrightarrow{B.}\overrightarrow{A}=BA\cos \varphi \]
The area which the conductor covers can be written as the product of velocity and length, so, the equation becomes
\[\Rightarrow e=Blv\cos \phi \]
But we are interested in finding out the rate at which the electrical energy converted into thermal energy in the resistance of the bar after the terminal velocity has been reached.
So, we need to find the rate of generation of thermal energy.
Using the formula,
\[\Rightarrow P=\dfrac{{{V}^{2}}}{R}\] where V is the emf generated and R is the resistance of the conductor.
\[\therefore P=\dfrac{{{B}^{2}}{{l}^{2}}{{v}^{2}}{{\cos }^{2}}\phi }{R}\]
So, the correct option is (B).
Note: If there was no change in the magnetic flux then there would have been no emf induced in the conductor. Since flux is the dot product of magnetic field and area vector, to change the flux there can be three conditions:
- Change in a magnetic field.
-Change in the area of the conductor.
-Change in the angle between the magnetic field and the area vector.
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)