A PowerPoint Presentation by: Upadhyaya Priyanka P. 13BECEG071 Vaibhavi Gosai J. 13BECEG065

1. A PowerPoint Presentation by: Upadhyaya Priyanka P. 13BECEG071 Vaibhavi Gosai J. 13BECEG065 Shivani Tare S. 13BECEG123

2. Calculate the magnitude and direction of the induced current or emf in a conductor moving with respect to a given B-field. • Calculate the magnetic flux through an area in a given B-field. • Apply Lenz’s law and the right-hand rule to determine directions of induced emf. • Describe the operation and use of ac and dc generators or motors.

3. What Is Electromagnetic Induction? The phenomenon of the production of induced emf in the circuit caused due to the change in the flux linking with the circuit is called Electromagnetic induction.

4. B I Down I Up Down Up v F B B F v When a conductor moves across flux lines, magnetic forces on the free electrons induce an electric current. Right-hand force rule shows current outward for down and inward for up motion. (Verify)

5. Faraday’s observations: B Flux lines  in Wb N turns; velocityv Faraday’s Law: • Relative motion of conductor in B-field induces emf. • Direction of emf depends on direction of motion. • Emf is proportional to rate at which lines are cut. • Emfis proportional to the number of turns N. The negative sign means that E opposes its cause.

6.  A Magnetic Flux density: • Magnetic flux lines are continuous and closed. • Direction is that of the B vector at any point. When area A is perpendicular to flux: The unit of flux density is the weber per square meter.

7. n A   B The flux penetrating the area A when the normal vector n makes an angle of  with the B-field is: The angle  is the complement of the angle  that the plane of the area makes with B field. (Cos  = Sin )

8. Faraday's Laws First Law: Whenever a flux linking with a coil or a circuit changes there is an emf induced in that coil or circuit. Second Law: Magnitude of the emf that is induced is proportional to the rate of change of flux linkages.

9. A change in flux can occur by a change in area or by a change in the B-field: Faraday’s Law:  = B A  = A B Rotating loop = B A Loop at rest = A B n n n

10. Induced B Induced B Left motion I Right motion N S N S I Lenz’s law: An induced current will be in such a direction as to produce a magnetic field that will oppose the motion of the magnetic field that is producing it. Flux increasing to left induces loop flux to the right. Flux decreasing by right move induces loop flux to the left.

11. x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx I v v x I x xxxxxxxxxxxxxxxxx I B v v B Induced emf Lenz’s law Directions Of ForcesAnd Emf: I An emf E is induced by moving wire at velocity v in constant B field. Note direction of I. L From Lenz’s law, we see that a reverse field (out) is created. This field causes a leftward force on the wire that offers resistance to the motion. Use right-hand force rule to show this.

12. Types Of Induced Emf Induced emf are of two types: 1.Dynamically induced emf 2.statically induced emf

13. Dynamically Induced Emf The Magnetic field is stationary and a conductor moves across the field. (a) shows a conductor 'X' of length 'l' lying in a stationary magnetic field of B Web/m2. Area, A=dx*l m2,Flux cut by the conductor,dφ=B*A=Bldx Emf induced e=dφ/dt=Bldx/dt=Blv volts • (b) shows the conductor having moved not perpendicular to the magnetic field but at an angle 'Θ' to direction of magnetic field. • Thus component of v perpendicular to lines of flux will be vsinθ • e=Blvsinθ

14. Statically Induced Emf • The conductor is stationary and the magnetic field is changing. • A circuit is consisting of N-turns coil connected to a battery and a switch ‘K’. • When switch ‘K’ is closed, current will increase from zero to maximum, flux linking will increase, so an emf is induced according to Faraday’s laws. • It would delay in the growth of current according to Lenz’s laws. • Thus, the emf induced in a coil due to change of flux linking with itself is called the self induced emf.

15. Mutually Induced Emf • A circuit consisting of two coils that are placed close to each other but are insulated from each other, • Coil connected to a battery and a switch ‘K’ is called primary coil and coil connected to a galvanometer is called secondary coil. • On performing switch, it can be seen that when the current in one coil is changed, there is an emf induced in a nearby coil. This is called mutually induced emf.

16. x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx I F B I L v v x B  v sin  v Induced Emf E Force F on chargeqin wire: F = qvB; Work = FL = qvBL EMF: If wire of length L moves with velocity v an angle  with B:

17. B v I I v B • An alternating AC current is produced by rotating a loop in a constant B-field. Rotating Loop in B-field • Current on left is outward by right-hand rule. • The right segment has an inward current. • When loop is vertical, the current is zero. Iin Ris right, zero, left, and then zero as loop rotates.

18. I=0 I=0

19. Rectangular loop a x b . n n a B  B b  b/2 v x Area A = ab v = r n  B v r = b/2  x vsin  Each segment a has constant velocity v. Both segments amoving with v at angle with B gives emf:

20. x . x . +E -E The emf varies sinusoidally with max and min emf For N turns, the EMF is:

21. The simple ac generator can be converted to a dc generator by using a single split-ring commutator to reverse connections twice per revolution. Commutator E t DC Generator For the dc generator: The emf fluctuates in magnitude, but always has the same direction (polarity).

22. Eb I V Electric Motor In a simple electric motor, a current loop experiences a torque which produces rotational motion. Such motion induces a back emf to oppose the motion. Applied voltage – back emf = net voltage V – Eb = IR Since back emf Eb increases with rotational frequency, the starting current is high and the operating current is low: Eb= NBA sin 

23. Motor In the commercial motor, many coils of wire around the armature will produce a smooth torque. (Note directions of I in wires.) Series-Wound Motor: The field and armature wiring are connected in series. Shunt-Wound Motor: The field windings and the armature windings are connected in parallel.