1 / 25

EE3321 ELECTROMAGENTIC FIELD THEORY

EE3321 ELECTROMAGENTIC FIELD THEORY. Week 8 Faraday’s Law Inductance Energy. Faraday's Law of Induction. The law states that the induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit: where

sumi
Download Presentation

EE3321 ELECTROMAGENTIC FIELD THEORY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EE3321 ELECTROMAGENTIC FIELD THEORY Week 8 Faraday’s Law Inductance Energy

  2. Faraday's Law of Induction • The law states that the induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit: where • Ɛ is the electromotive force (EMF) in Volts • ΦB is the magnetic flux through the circuit in Webers

  3. Magnetic Flux • The magnetic flux ΦB through a surface S, is defined by an integral over a surface:

  4. Example

  5. Analysis • If the loop enters the field at a constant speed, the flux will increase linearly and EMF will be constant. • What happens when the entire loop is in the field?

  6. Exercise • A conducting rod of length L moves in the x-direction at a speed vax as show below. • The wire cuts into a magnetic field B az. • Calculate the induced EMF.

  7. Procedure • Compute the total flux ΦB ΦB = B A = B L (xo + vt) • Calculate the rate of change Ɛ = -dΦB/dt = - vBL • Since the magnetic flux through the loop increases linearly the EMF induced in the loop must be constant.

  8. AC Generator • An EMF is induced on the rectangular loop of the generator. • The loop of area A is rotating at an angular rate ω (rads). • The magnetic field B is held constant.

  9. Exercise • Assume B = Boax • the square loop rotates so its normal unit vector is an = axcosωt + ay sin ωt • Determine the flux as a function of time and the induced EMF

  10. Inductance • Inductance is the property in an electrical circuit where a change in the current flowing through that circuit induces an EMF that opposes the change in current.

  11. EE (Heaviside) Notation • The term 'inductance' was coined by Oliver Heaviside. It is customary to use the symbol L for inductance, possibly in honor of Heinrich Lenz. • Other terms coined by Heaviside • Conductance G • Impedance Z • Permeability μ • Reluctance R

  12. Inductance • The electric current produces a magnetic field and generates a total magnetic flux Φ acting on the circuit. • This magnetic flux tends to act to oppose changes in the flux by generating an EMF that counters or tends to reduce the rate of change in the current. • The ratio of the magnetic flux to the current is called the self-inductance which is usually simply referred to as the inductance of the circuit.

  13. Example • Derive an expression for the inductance of a solenoid Since B = μNI/ℓ Φ = BA = μNIA/ℓ thus L = NΦ/I = μN2A/ℓ

  14. Exercise • Derive an expression for the inductance of a toroid. Recall that B = μNI 2πr

  15. Magnetic Pickups • The pickup from an electric guitar captures mechanical vibrations from the strings and converts them to an electrical signal. • The vibration from a string modulates the magnetic flux, inducing an alternating electric current.

  16. Flux Linkage • Taking the time derivative of the flux linkage λ = NΦ = Li yields = v This means that, for a steady applied voltage v, the current changes in a linear.

  17. Exercise • Let the current through an inductor be i(t) = Iocos(ωt). Determine v(t) across the inductor.

  18. Ferromagnetic Core • In practice, small inductors for electronics use may be made with air cores. • For larger values of inductance and for transformers, iron is used as a core material. • The relative permeability of magnetic iron is around 200.

  19. Ferromagnetic Materials

  20. Mutual Inductance • Here, L11 and L22 are the self-inductances of circuit one and circuit two, respectively. It can be shown that the other two coefficients are equal: L12 = L21 = M, where M is called the mutual inductance of the pair of circuits.

  21. Flux Coupling • Consider for example two circuits carrying the currents i1, i2. • The flux linkages of circuits 1 and 2 are given by L12 = L21 = M

  22. Example • Describe what will happen when the switch is on.

  23. Energy • The energy density of a magnetic field is u = B2 2μ • The energy stored in amagnetic field is U = ½ LI2

  24. Exercise: • In a certain region of space, the magnetic field has a value of 10-2 T, and the electric field has a value of 2x106 V/m. • What is the combined energy density of the electric and magnetic fields?

  25. Homework • Read Sections 6-1, 6-2, 6-4, and 6-5. • Solve end-of-chapter problems 6.2, 6.5, 6.10, and 6.12.

More Related