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# Electromagnetic Induction - EMI - 12th JEE Preparation Tips

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### Electromagnetic Induction - EMI - 12th JEE Preparation Tips

1. 1. 9011041155 / 9011031155 • Live Webinars (online lectures) with recordings. • Online Query Solving • Online MCQ tests with detailed solutions • Online Notes and Solved Exercises • Career Counseling 1
2. 2. 9011041155 / 9011031155 Electromagnetic Induction electromagnetic induction with the help of Faraday’s expt. Ans: Change in the magnetic flux linked with the coil produces emf in the coil, which causes electric current to flow through it. This emf is called induced emf and the current is called induced current. Production of induced emf in the coil due to change in the magnetic field associated with it is called electromagnetic induction. Coil and Magnet experiment 2
3. 3. 9011041155 / 9011031155 Coil and Coil experiment : 3
4. 4. 9011041155 / 9011031155 Faraday’s laws of electromagnetic induction. Ans: 1. Whenever there is change in the magnetic field associated with a coil, an emf in induced in it. 2. The magnitude of this emf is directly proportional to the rate of change of flux associated with it. d dt e e or e d k dt d dt 4
5. 5. 9011041155 / 9011031155 Lenz’s law. Ans “The direction of induced emf is such as to oppose the change in the magnetic flux which produces it.” e d dt Thus, faraday’s law gives the magnitude and Lenz’s law gives the direction of induced emf. 5
6. 6. 9011041155 / 9011031155 theoretical proof of laws of electromagnetic induction. Ans: The mathematical statement of the laws of induction is e d dt F = q v × B, to it. Hence, it is acted up on by a force F’ given by F’ = Biℓ sin θ . But as θ = π/2, sin θ = 1 and the force is F’ = Biℓ 6
7. 7. 9011041155 / 9011031155 the work dW done in this process is dW = -F’dx ( -ve sign as the force is applied opposite to F’) ∴ dW = - Biℓ × dx But, ℓ × dx is the area A of the frame swept by the force. ∴ dW = - BiA If dφ is the magnetic flux through area A, B = dφ ℓ A ∴ dφ = BA ∴ dW = - i dφ------(1) If e is the induced emf and i is the induced current, the electrical power generated in the frame is p = ei If this power is generated in time dt, 7
8. 8. 9011041155 / 9011031155 electrical work done = eidt-----(2) This work must be equal to the work done by force F’ ∴ eidt = - idφ----- from 1 &2 e d dt Hence, the laws of electromagnetic induction are proved. As e d dt BA dt dx B dt 8 Bv
9. 9. 9011041155 / 9011031155 Fleming’s right hand rule. Ans: 9
10. 10. 9011041155 / 9011031155 Eddy currents Ans: Applications : 1. Dead beat galvanometer 10
11. 11. 9011041155 / 9011031155 2. Induction Furnace i. fast operation ii. better control over the temperature iii. surface heating iv. less pollution etc. 11
12. 12. 9011041155 / 9011031155 3. Electric brakes 12
13. 13. 9011041155 / 9011031155 M.C.Q. A coil having an area of 2m2 is placed in a magnetic field which changes from 2Wb/m2 to 5Wb/m2 in 3s. The e.m.f. induced in the coil will Be (a.6) 4V (b.6) 3V (c.6) 2V (d.6) 1V Q.7 The magnetic flux in a coil is Ф= 4t2 + 4t + 4. What is the magnitude of induced e.m.f. at t=3sec? (a.7) 14V (b.7) 28V (c.7) 7V (d.7) 35V Q.6 Q.8 The two rails of a railway track separated by 1metre and insulated from each other, are connected to a millivoltmeter. What is the reading of the millivoltmeter when a train passes at a speed of 180km/hour along the track? [The vertical component of earth’s magnetic field is 0.2×10-4Wb/m2] (a.8) 1volt (b.8) 100mV (c.8) 1mV (d.8) 10mV 13
14. 14. 9011041155 / 9011031155 Self inductance. Ans: Production of induced emf in a coil due to changing magnetic flux produced due the varying current in the coil itself is called self induction. Flux φ associated with the coil is proportional to current i in the coil. i.e. φ α i or φ = Li where L is a constant which depends on size and shape of the coil. The induced emf generated in the coil is given as 14
15. 15. 9011041155 / 9011031155 d Li d dt e L dt di dt The constant L is called self inductance of the coil. If di/dt = 1, them e = - L “Thus, self inductance of a coil is equal to the emf induced in the coil, due to unit rate of change of current through it”. L e di / dt The unit of self inductance is henry (H). 1 henry 1 volt 1 ampere / 1 second 1 henry :The self inductance of a coil is 1 henry, if the emf of 1V is induced in the coil, when the current through the coil changes at 1 ampere per second. 15
16. 16. 9011041155 / 9011031155 Mutual inductance. Ans: Production of induced emf in a coil due to changes in current in the second coil near it is called mutual induction. i.e. e2 dIA dt dI A M dt e2 When dIA /dt = 1, e2 = - M 16
17. 17. 9011041155 / 9011031155 Thus, mutual inductance between two coils is equal to the emf induced in the second coil due to unit rate of change of current in the first coil. M e2 dIA / dt The unit of mutual inductance is henry (H). 1 henry 1 volt 1 ampere / 1 second 1 henry : The mutual inductance between two coils is 1 henry, if the emf of 1V is induced in the second coil, when the current through the first coil changes at 1 ampere per second. 17
18. 18. 9011041155 / 9011031155 Transformer action. E1 d N1 dt and E2 d N1 dt 18 N1 N2 d dt d dt
19. 19. 9011041155 / 9011031155 E2 E1 N2 N1 E.M.F. induced across secondary E.M.F. induced across primary Number of turns of the secondary coil Number of turns of the primary coil Power output = Power input E2I2 = E1I1 E2 E1 I1 I2 N2 N1 % efficiency Output power Input power 19 100%
20. 20. 9011041155 / 9011031155 20
21. 21. 9011041155 / 9011031155 • Ask Your Doubts • For inquiry and registration, call 9011041155 / 9011031155. 21