U3AOS3 Topic 2: EMF and Faraday

E.M.F


EMF stands for Electromotive Force. The electric potential produced by an electrochemical cell or by changing the magnetic field is called EMF.


EMF is the potential difference between two point charges in a circuit.


  • Like its name, EMF is not a force. It is the Energy per unit charge (EMF= E/Q) where W is work done and Q is charge enclosed in a circuit.


  • Its unit is Volt (V).


  • It is measured through voltmeter.






Sources of EMF:


  • Batteries or cells convert chemical energy into electric energy

  • Electric generators convert mechanical energy into electric energy.

  • Thermocouples convert heat energy into electric energy.

  • Photovoltaic cells convert solar energy into electric energy.


Examples:


  1. Flashlight: The electromagnetic field (EMF) is generated by the charge of the batteries in the flashlight to illuminate the bulb.

  2. Autos: Car batteries supply the EMF needed to start the engine and run the electrical systems.

  3. Appliances inside the home: During power outages, EMF are provided by home generators.



     Induced EMF:



Induced EMF is the electromotive force generated in a conductor due to a change in magnetic flux through it. This can occur through relative motion between a magnet and the conductor or by changing the magnetic field strength.

Example:

When a magnet is moved towards or away from a coil of wire, the changing magnetic field through the coil induces a voltage (EMF) in the coil. This principle is used in electric generators where rotating coils in a magnetic field generate electricity



         Motional EMF:




 The induced e.m.f. Due to the motion of an electric conductor in the presence of a magnetic field is called motional e.m.f.



                             E= Blv    (B,l and v are perpendicular to each other)


The e.m.f. generated in a circuit by the moving rod is simply the product of the magnetic field strength, the length of the rod and the velocity of the rod.



Motional e.m.f is an example of dynamically induced e.m.f. It is so called because e.m.f is induced in the conductor which is in motion.



Explanation:


Consider a conducting rod PQ placed in a uniform magnetic field directed into the page. The rectangle PQRS from a closed circuit enclosing a varying area due to the motion of the rod PQ.



Using Faraday’s law of induction to find the magnitude of E.M.F induced along the moving rod,

                                 E= N ΔΦ/Δt



                            E= (1) Δ(BA cos)  /Δt



                            E= (1) Δ(BA cos0)  /Δt



                            E= (1) Δ(BA)  /Δt



                            E= BΔA  /Δt



The area enclosed by the circuit PQRS is ΔA =lΔx


                                       E= B(lΔx) /Δt


The velocity of the rod is v= Δx /Δt, thus,

                                          

                                   E=Blv


                                                                     


                                          Faraday’s Law:




The practical demonstration of electromagnetic induction prove that E.M.F induced in a coil depend upon the following factors:


  1. E.M.F is directly proportional to the rate of change of magnetic flux through the coil ,greater is induced E.M.F.


                                E=dΦ/dt



  1. E.M.F is directly proportional to the number of turns N in the coil. E∝N

                                         

                                E ∝ dΦ/dt



                        E= k N dΦ/dt                        (k=1)



                        E= - N   dΦ/dt


The equation of induced E.M.F is called Faraday Law of induction.


The induced E.M.F always opposes the change in flux. The direction of induced E.M.F is given by Lenz’s law. 



                                 E= - N dΦ/dt


The negative sign in the equation represents Lenz’s Law.

Applications:

  1. Electric Generators: It converts mechanical energy to electrical energy using rotating coils in a magnetic field.

  2. Transformers: It transfers electrical energy between circuits through electromagnetic induction.

  3. Induction Cooktops: It generates heat directly in the cookware using induced currents.


Practical Example:

When a magnet is moved towards a coil of wire, the changing magnetic field induces an EMF in the coil, generating a current if the circuit is closed.


                                                      


                                      

Example 1
Cell, thermocouple, generator etc are examples of sources of emf.  In nature, emf is generated when magnetic field fluctuations occur through a surface.


 


Example 2

A coil with 50 turns (N) is placed in a magnetic field that changes from 0.2 T to 0.8 T in 4 seconds. The area of the coil (A) is 0.1 m². Calculate the induced EMF.




Solution:

  1. Calculate the change in magnetic flux (ΔΦ𝐵):ΔΦ𝐵=𝐵final⋅𝐴−𝐵initial⋅𝐴ΔΦ𝐵=(0.8 T⋅0.1 m2)−(0.2 T⋅0.1 m2)ΔΦ𝐵=0.08 Wb−0.02 Wb=0.06 Wb



Use Faraday's Law to calculate the induced EMF:𝐸=−𝑁ΔΦ𝐵Δ𝑡

𝐸=−500.06 Wb4 s

𝐸=−50⋅0.015 V=−0.75 V

The induced EMF is −0.75 V (the negative sign indicates the direction according to Lenz's Law).


Example 3
A metal rod of length 1.5 meters moves perpendicular to a magnetic field of 0.4 T at a speed of 2 m/s. Calculate the induced EMF.
E=0.4 T⋅2 m/s⋅1.5 m\mathcal{E} = 0.4 \, \text{T} \cdot 2 \, \text{m/s} \cdot 1.5 \, \text{m} E=1.2 V\mathcal{E} = 1.2 \, \text{V}
Example 4
A magnetic field through a 0.4 m² loop changes from 2 T to 1.5 T in 3 seconds. The loop has 120 turns. Calculate the induced EMF.


Example 5

ΔΦB=(0.1 T−0.6 T)⋅0.06 m2=−0.03 Wb\Delta \Phi_B = (0.1 \, \text{T} - 0.6 \, \text{T}) \cdot 0.06 \, \text{m}^2 = -0.03 \, \text{Wb} E=−50⋅−0.03 Wb5 s=0.3 V\mathcal{E} = -50 \cdot \frac{-0.03 \, \text{Wb}}{5 \, \text{s}} = 0.3 \, \text{V}
Example 6
A coil with 200 turns and a cross-sectional area of 0.02 m² is placed in a magnetic field that changes from 0.5 T to 1.0 T in 6 seconds. Calculate the induced EMF.
E=−NΔΦBΔt\mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t} E=−2000.01 Wb6 s=−0.33 V\mathcal{E} = -200 \frac{0.01 \, \text{Wb}}{6 \, \text{s}} = -0.33 \, \text{V}
Exercise &&1&& (&&1&& Question)

What is EMF?

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Exercise &&2&& (&&1&& Question)

 EMF stands for _____ according to Faraday law

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Exercise &&3&& (&&1&& Question)

A straight line conductor of length 0. 4m is moved with a speed of 7ms-1 perpendicular to a magnetic field of an intensity of 0.9wbm-2  The induced emf across the conductor is

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Exercise &&4&& (&&1&& Question)

Find out the electromotive force of a circuit with energy and charge of 2400 J and 10 C.

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Exercise &&5&& (&&1&& Question)

Calculate the motional E.M.F induced along a 20.0 km conductor moving at an orbital speed of 7.80 km/s  perpendicular to Earth 5.00x105 T magnetic field. 
−5 T magnetic field.


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Exercise &&6&& (&&1&& Question)

A metal rod of length 2 meters moves perpendicular to a magnetic field of 0.5 T at a speed of 3 m/s. Calculate the induced EMF.

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Exercise &&7&& (&&1&& Question)

A solenoid with 150 turns and a cross-sectional area of 0.01 m experiences a change in magnetic flux from 0.5 Wb to 0.2 Wb over a period of 3 seconds. Calculate the induced EMF.

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Exercise &&8&& (&&1&& Question)

A coil with 100 turns (N) is placed in a magnetic field that changes from 0.3 T to 1.2 T in 5 seconds. The area of the coil is 2m. Calculate the induced EMF.

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Exercise &&9&& (&&1&& Question)

A coil with 50 turns (N) experiences a change in magnetic flux from 0.1 Wb to 0.3 Wb in 4 seconds. Calculate the induced EMF.

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