Introduction to Electromagnetism

Transcription

1 Introduction to Electromagnetism

2 Electric Field Lines If a charge feels an electrostatic force (Coulombic Force), it is said to be in an electric field. We like to represent electric fields with lines. The lines basically show where a positive test charge would feel a force. The lines also go off into infinity! The farther apart the lines, the weaker the field; the closer the lines, the stronger the field. The electric field lines of a positive charge point outwards and negative charge point inwards Like charges repel (Force is +), unlike attract (Force is -) + q - q

3 Magnetic field The magnetic force exerted in the region around the magnet is the magnetic field. Direction of magnetic field at any point is defined as the direction of motion of a charged particle on which the magnetic field would not exert a force Magnetic field lines show the direction of the field and it always go from the N pole to the S pole. Magnetic fields are vector quantities i.e., they have a magnitude and a direction written as B S N Strongest field at poles

4 Magnetic Flux, Φ The group of force lines going from the N pole to the S pole of a magnet is called the magnetic flux, symbolized by Φ. No. of magnetic field lines determines the value of the flux. The more lines of force, the greater the flux and the stronger the magnetic field. Unit of magnetic flux is the weber (Wb); One weber = 10 8 lines. Magnetic Flux Density, (B) is the amount of flux per unit area (i.e. B = Φ/A) perpendicular to the magnetic field. Unit 1 tesla (T) = one weber/square meter.

5 The Earth is a magnet William Gilbert, an English physician, i first proposed in 1600 that the earth itself is a magnet, and he predicted that the earth would be found to have magnetic poles. The Earth has an immense magnetic field around it called the magnetosphere. The circulation of the molten iron and nickel in the Earth s outer core produces a magnetic field. It exerts magnetic forces and is strongest near the North and South magnetic poles. A compass s needle points to the north geographic pole due to the south magnetic pole being nearby.

6 Origin of AURORA BOREALIS and AURORA AUSTRALIS Aurora Borealis Aurora Australis They are formed when charged particles from the sun (known as solar wind) hit oxygen and nitrogen atoms in the air. The atoms become excited and then give off many colors of light. The reason for the appearance at the poles is that the Earth s magnetic poles pull the sun s high- speed, charged particles towards them. North Pole - Northern lights: aurora borealis South Pole - Southern lights: aurora australis

7 Electromagnetism Explain the connection between electricity and magnetism A changing magnetic field produces an electric field, and a changing electric field produces a magnetic field. Electric and Magnetic fields can produce forces on charges An accelerating charge produces electromagnetic waves (radiation) Both electric and magnetic fields can transport energy Electric field energy used in electrical circuits, e.g., released in lightning Magnetic field carries energy through transformer.

8 Electric Current and Magnetism connection For a long time, magnetism and electricity were thought to be separate phenomena in nature. April 1820: Hans Christian Ørsted discovers deflection of compass needle when close to a wire carrying a current just as if the wire were e a magnet. When the battery was off the needle return to the true north.

9 Oersted s Law The flow of electricity through a wire conductor produces a magnetic field around the wire. Implication: the current carrying wire itself behaves like a magnet (since it can exert a force on another magnet like a permanent magnet would). An application of Oersted s Effect is the electromagnet and all the devices using it such as telephone receiver, speaker, electrical motors etc.

10 Biot-Savart Law In 1820, Jean-Baptiste Biot and Felix Savart published their observations that current in a wire induced a magnetic field around the wire. They noticed that the field was perpendicular to both the direction of current and the radius of the wire, leading to a precise mathematical form of the Biot-Savart Law. (B is the magnitude of the magnetic field produced by current I). B long wire μ 0 is the permeability of free space. 0 I 2r Right-hand rule

11 Ampère s Law Ampère s law relates the magnetic field around a closed loop to the total current flowing through the loop. September 1820: André-Marie Ampère publishes mathematical explanation of Ørsted s oberservation, now known as Ampère s Law. Ampère s Law states that along any closed path through a magnetic field, the sum of the products of the scalar component of B is directly proportional to the net electric current passing through hth the area enclosed db by the path.

12 Electromagnets An electromagnet is a type of magnet. The magnetic field is produced by the flow of electric current. The magnetic field is porportional to The number of turns in the winding The current in the wire Enhanced by a iron core

13 Faraday s Laws of EM Induction Michael Faraday was an experimental scientist discovered the principle of electromagnetic induction in Faraday's two observations in EM induction: 1) The amount of voltage induced in a coil is directly proportional to the rate of change of the magnetic field w.r.t. the coil. 2) The amount of voltage induced in a coil is directly proportional to the no. of turns of wire in the coil. If a circuit contains N tightly wound loops and the flux changes by ΔΦ B during a time interval Δt, the average emf induced is given by Faraday s Law: N t B

14 Application of Faraday s Law AC generator simulation

15 Maxwells s Electromagnetic Equations

16 Maxwell s Theory for electromagnetism In 1865, James Clerk Maxwell developed a theory of electricity and magnetism. Found a way to account for the phenomena of electricity, magnetism, and light itself, in a single system of wave equations. Electric and magnetic fields travel through space in the form of waves at the speed of light. A changing magnetic field will induce a changing g electric field, and vice versa.

17 Maxwell s Theory His starting points were: 1. Electric field lines originate on + charges and terminate on - charges 2. Magnetic field lines form closed loops 3. A varying magnetic field induces an electric field 4. A magnetic field is created by a current

18 Gauss s Law Electricity The total flux within a closed surface is proportional to the enclosed charge. E da = Q enclosed 0 Gauss s Law is always true, but is only useful for certain very simple problems with great symmetry.

19 E Maxwell s 1 st Equation 0 Equivalent to Gauss Flux Theorem: E E dv E ds 1 0 V S 0 V dv Q The flux of electric field out of a closed region is proportional to the total electric charge Q enclosed within the surface. A point charge q generates an electric field sphere q E r r q ds q EdS 2 4 r 0 sphere Area integral gives a measure of the net charge enclosed. 0 0

20 Gauss s Law for Magnetism Since there are no magnetic monopoles there is no place for magnetic field lines to begin or end. Gauss, states that an enclosed magnet will have a net magnetic flux (B) of zero. Thus, Gauss ss Lawfor magnetic charges must be: B da 0 Every magnet has a north pole and a south pole, so that if you were to enclose even a part of a magnet within a soap bubble, the total number of magnetic field lines entering the bubble would equal the total number of magnetic field lines exiting the bubble, with a net of zero.

21 B 0 Maxwell s 2 nd Equation Gauss law for magnetism: B 0 B ds 0 There are no magnetic monopoles The net magnetic flux out of any closed surface is zero. Surround a magnetic dipole with a closed surface. The magnetic flux directed inward towards the south pole will equal the flux outward from the north pole. If there were a magnetic monopole source, this would give a non-zero integral.

22 Faraday s Law of Induction A changing g magnetic field creates an electric field. is the electromotive force (EMF) in volts is the magnetic flux through the circuit (in webers) A change in flux of one weber per second will induce EMF of 1 volt.

23 E B t Maxwell s 3 rd Equation Equivalent to Faraday s LawofInduction: B E ds ds t S S d d E dl B ds dt dt C (for a fixed circuit C) The electromotive force round a E dl circuit is proportional to the rate of change of flux of magnetic field, B ds S through the circuit. Faraday s Law is the basis for electric generators. It also forms the basis for inductors and transformers. N S

24 Ampère-Maxwell Law Oersted and Ampere and Gauss showed that a current (I) would create a magnetic field (B). Hence, Bdl 0 I Steady current implies constant charge density so Ampere s law consistent with the Continuity equation for steady currents. However, Maxwell took it further and showed that a magnetic field (B) is created by a current (I) and a changing electric field (d E /dt). Therefore, Maxwell s revision of Ampere s Law becomes... Bdl 0I00 ddt E

25 B dl 0I 00 ddt E Maxwell s 4 th Equation Oii Originates from Ampère s (Circuital) it Law : B dl B ds C S S 0 j ds I 0 Satisfied by the field for a steady line current (Biot- Savart Law, 1820): 0I dl r B 3 4 r For a straight line current B 0I 2 r

26 Changing E field creates B field! Faraday: Varying B-field generate E-field Maxwell: varying E-field should then produce a B-field, but not covered by Ampère s Law. Surface 1 Surface 2 Apply Ampère to surface 1 (flat disk): line integral of B = 0 I Current I Closed loop Applied to surface 2, line integral is zero since no current penetrates the deformed surface. E Q ε A In capacitor,, so Displacement current density is 0 dq de A dt E dt j d 0 t I 0 26

27 Maxwell solved this problem by realizing that... Inside the capacitor there must be an induced magnetic field... B E How?. Inside the capacitor there is a changing E A changing electric field induces a magnetic field Therefore, Maxwell s revision of Ampere s Law becomes... d Bdl E 00 I 0 dt where I d is called the displacement current B dl I d ddt E 0 0 0

28 Maxwell s Equations of Electromagnetism q Gauss Law for Electrostatics E da 0 Gauss Law for Magnetism Faraday s Law of Induction B da 0 E dl ddt d B Revised da Ampere s Law B dl I d dt E

29 Electromagnetic Waves let there be light. B B dl d d E E dl B 0 0 dt dt v de dt E db dt These two equations can be solved simultaneously give plane waves resulting in EM waves E(x, t) = E max sin (kx-t)ĵ B(x, t) = B max sin (kx-t)ẑ

30 B z Plane Electromagnetic Waves E y Alternating electric field induces alternating magnetic field & vice versa. Self-propagating electromagnetic disturbance = light. c E(x, t) = E max sin (kx-t) jˆ B(x, t) = B max sin (kx-t) ẑz x

31 Properties of EM Waves The radiated EM waves have certain properties: EM waves all travel at the speed of light c. The E and B fields are perpendicular to each other. The E and B fields are in phase (both reach a maximum and minimum at the same time). The E and B fields are perpendicular to the direction of travel (transverse waves).

32 The Electromagnetic Spectrum There are many more forms of electromagnetic radiation than just visible light. The visible band we know is a pretty small section bt between ultraviolet ilt(uv) and dif infrared d(ir) (IR).

33 Production of Electromagnetic Waves Oscillating charges will produce electromagnetic waves. When Maxwell calculated the speed of propagation of electromagnetic waves, he found: This is the speed of light in a vacuum. Over the years, measurements have become more and more precise; now the speed of light is defined to be: In 1888, Heinrich Hertz demonstrated the existence of electromagnetic waves and proved Maxwell s theory.