Faraday's law of Electromagnetic Induction

1. Course: Electromagnetic Theory Arpan Deyasi A Deyasi & Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India Electromagnetic paper code: EC 501 P Debnath Topic: Electromagnetic Induction Theory Course Coordinator: Arpan Deyasi 25-10-2024 Arpan Deyasi, EM Thoery 1

2. Laws of Induction [i] When a closed loop moves and is deformed in an external magnetic field, e.m.f is induced in it. Arpan Deyasi A Deyasi & d Ndt [ii] Induced e.m.f is numerically equal to the time rate of variation of magnetic flux of external field through the surface stretched over the closed loop. Electromagnetic P Debnath Theory [iii] Direction of induced e.m.f is such that magnetic flux associated with the current generated by it, opposes the original change of flux causing the e.m.f   = − Lenz’s Law 25-10-2024 Arpan Deyasi, EM Thoery 2

3. Lenz’s Law Arpan Deyasi B ΔB A Deyasi & S N ΔB B Electromagnetic I N S I Bind N S Bind P Debnath Theory B ΔB ΔB B I S N I Bind Bind 25-10-2024 Arpan Deyasi, EM Thoery 3

4. Faraday’s Law  d Lenz’s law is given by Arpan Deyasi  = − Ndt A Deyasi &    = −   = Electromagnetic  = E.dl B.ds Induced emf Magnetic flux P Debnath E N Theory d dt   = − E.dl N B.ds   ( ) B t   = − E .ds N .ds B t 25-10-2024 Arpan Deyasi, EM Thoery 4

5. Prob 1: Magnetic field acts downwards at an angle 30⁰ to the vertical on a square loop of side 5 cm. Induction is 0.5 Wb.m-2. Calculate average induced emf, if field increases from 0 to final value in 0.1 sec. Arpan Deyasi A Deyasi & d dt Electromagnetic Soln: − − = (5 10 )  2 2 P Debnath A m Area of the loop Linked magnetic flux Theory  =  ABcos( ) −  =  3 1.08 10 Wb   = −  =  2 1.08 10 volt Induced emf 25-10-2024 Arpan Deyasi, EM Thoery 5

6. Relation between Electric Field and Potentials Arpan Deyasi = B A Magnetic field is related with vector potential as Electromagnetic A Deyasi & E  +    B t A t  = P Debnath Theory  A t  = − E  A t  = 0 25-10-2024 Arpan Deyasi, EM Thoery 6

7. Relation between Electric Field and Potentials Arpan Deyasi        A t   + = E 0 A Deyasi & t  Electromagnetic P Debnath E = −−  = E 0 eff Theory = − A = − E eff  + E  A t  25-10-2024 Arpan Deyasi, EM Thoery 7

8. Relation between Electric Field and Potentials Arpan Deyasi  A Deyasi & A t  = −− E Electromagnetic P Debnath First term in RHS depicts that static charges are one of the possible source of electric field; whereas the second term in RHS signifies that time varying magnetic field is another possible Source of electric field. Theory 25-10-2024 Arpan Deyasi, EM Thoery 8

9. Prob 2: A coil of resistance 100 Ω is placed in a magnetic flux of 105 emu per turn. The coil has 100 turns. A galvanometer of resistance 900 Ω is connected in series with it. Find induced emf and current in the coil if the coil is moved in 0.1 sec from the given flux to a flux of 2⨯ ⨯104 emu per turn. Arpan Deyasi A Deyasi & Total circuit resistance R (100 900) = Electromagnetic Soln:  = 2 10 ) emu −  P Debnath Current in the coil I 5 4 d (10 Change in flux Theory −  = 0.8 10  3 d Wb  d dt  = 0.8 volt  = N Induced emf +   = = 0.8 mA R 25-10-2024 Arpan Deyasi, EM Thoery 9

10. Amount of charge flow due to induced emf Arpan Deyasi  d  = − Ndt N d R dt Induced emf A Deyasi & N Q R Induced current Electromagnetic   = = − I P Debnath R Theory  dq dt N d R dt = − ( ) =  − 1 2 25-10-2024 Arpan Deyasi, EM Thoery 10