The magnetic field through a coil having $ 200 $ turns and cross-sectional area $ 0.04{m^2} $ changes from $ 0.1Wb{m^{ - 2}} $ to $ 0.04Wb{m^{ - 2}} $ in $ 0.02\sec $ . Find the induced emf.
Answer
307.8k+ views
Hint An emf will be induced when the magnetic field changes. In other words, when the flux associated with a coil or a conductor changes there will be an induced emf. Emf means electromotive force that is the driving force of the current. Here the change in the magnetic field is given and we have to find the induced emf.
Complete step by step solution
The number of turns of the coil is given as, $ N = 200 $
The cross-sectional area of the coil is given by, $ A = 0.04{m^2} $
The magnetic field before changing is, $ {B_1} = 0.1Wb{m^{ - 2}} $
The magnetic field is changed to $ {B_2} = 0.04Wb{m^{ - 2}} $
The time is given as, $ t = 0.02\sec $
The induced emf is proportional to the rate of change of flux,
i.e, $ emf = \dfrac{{d\Phi }}{{dt}} = \dfrac{{ - d\left( \Phi \right)}}{{dt}} $
The flux can be written as,
$ \Phi = NBA $
where $ N $ stands for the number of turns, $ B $ stands for the magnetic field, and $ A $ stands for the cross-sectional area of the coil.
Substituting this value of $ \Phi $ in the above equation,
$ emf = - NA\dfrac{{dB}}{{dt}} $
The change in the magnetic field, $ dB = {B_2} - {B_1} $
The value of $ {B_1} $ is given as, $ {B_1} = 0.1Wb{m^{ - 2}} $
The value of $ {B_2} $ is given as, $ {B_2} = 0.04Wb{m^{ - 2}} $
The total number of turns in the coil is given as, $ N = 200 $
The area of cross-section of the coil is given as, $ A = 0.04{m^2} $
Substituting these values in the above equation,
The induced emf will be,
$ emf = - 200 \times 0.04 \times \dfrac{{0.04 - 0.1}}{{0.02}} = 24V $
The answer is: $ 24V $ .
Note
The external energy required to drive the free electrons in a particular direction is called the electromotive force. The emf is the work done in moving a unit positive charge from one end to the other. The rate of flow of charge is the electric current. The unit of emf is volt $ (V) $ or Joule/Coulomb $ (J/C) $ .
Complete step by step solution
The number of turns of the coil is given as, $ N = 200 $
The cross-sectional area of the coil is given by, $ A = 0.04{m^2} $
The magnetic field before changing is, $ {B_1} = 0.1Wb{m^{ - 2}} $
The magnetic field is changed to $ {B_2} = 0.04Wb{m^{ - 2}} $
The time is given as, $ t = 0.02\sec $
The induced emf is proportional to the rate of change of flux,
i.e, $ emf = \dfrac{{d\Phi }}{{dt}} = \dfrac{{ - d\left( \Phi \right)}}{{dt}} $
The flux can be written as,
$ \Phi = NBA $
where $ N $ stands for the number of turns, $ B $ stands for the magnetic field, and $ A $ stands for the cross-sectional area of the coil.
Substituting this value of $ \Phi $ in the above equation,
$ emf = - NA\dfrac{{dB}}{{dt}} $
The change in the magnetic field, $ dB = {B_2} - {B_1} $
The value of $ {B_1} $ is given as, $ {B_1} = 0.1Wb{m^{ - 2}} $
The value of $ {B_2} $ is given as, $ {B_2} = 0.04Wb{m^{ - 2}} $
The total number of turns in the coil is given as, $ N = 200 $
The area of cross-section of the coil is given as, $ A = 0.04{m^2} $
Substituting these values in the above equation,
The induced emf will be,
$ emf = - 200 \times 0.04 \times \dfrac{{0.04 - 0.1}}{{0.02}} = 24V $
The answer is: $ 24V $ .
Note
The external energy required to drive the free electrons in a particular direction is called the electromotive force. The emf is the work done in moving a unit positive charge from one end to the other. The rate of flow of charge is the electric current. The unit of emf is volt $ (V) $ or Joule/Coulomb $ (J/C) $ .
Last updated date: 29th Sep 2023
•
Total views: 307.8k
•
Views today: 8.07k
Recently Updated Pages
10 Examples of Evaporation in Daily Life with Explanations

10 Examples of Friction in Our Daily Life

Difference between hardware and software

What is the Full Form of DNA and RNA

10 Advantages and Disadvantages of Plastic

What are the Difference Between Acute and Chronic Disease

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
