Presentation on theme: "General electric flux definition"— Presentation transcript:
1 General electric flux definition The field is not uniformThe surface is not perpendicular to the fieldIf the surface is made up of amosaic of N little surfaces
2 Magnetic FluxWhenever possible:Units: [Weber] = [Wb]=[T-m2]
3 Gauss’s Law Gauss asserts that the calculation for the flux through a closed surface from a point charge is true for anycharge distribution!!!This is true so long as Q is the chargeenclosed by the surface of integration.
4 Gauss’s Law for magnetism This is true because we cannot isolate a magnetic pole and because magnetic field lines are continuous. The net number of field lines passing through any surface is always zero!
5 Faraday’s LawWhen the magnet moves, a current is induced as if there was a source of emf (like a battery) in the circuit!
9 Faraday’s Law of Induction An induced emf is produced by a changing magnetic field.Lenz’s Law – An induced emf is always in a direction that opposes the original change in the flux that caused the emf.Units: [Volts]
10 How can we change the flux? Change flux by:Change areaChange angleChange field
13 30. In Figure P31. 30, the bar magnet is moved toward the loop 30. In Figure P31.30, the bar magnet is moved toward the loop. Is Va – Vb positive, negative, or zero? Explain.Figure P31.30
14 Faraday’s Law – continued Remember FB is the magnetic flux through the circuit and is found byIf the circuit consists of N loops, all of the same area, and if FB is the flux through one loop, an emf is induced in every loop and Faraday’s law becomes
15 Decaying uniform magnetic field P31.4 Assume we can change field:ARChange flux by:Change fieldChange areaChange angle
16 Applications of Faraday’s Law – Pickup Coil The pickup coil of an electric guitar uses Faraday’s lawThe coil is placed near the vibrating string and causes a portion of the string to become magnetizedWhen the string vibrates at the same frequency, the magnetized segment produces a changing flux through the coilThe induced emf is fed to an amplifier
17 1. A 50-turn rectangular coil of dimensions 5. 00 cm × 10 1. A 50-turn rectangular coil of dimensions 5.00 cm × 10.0 cm is allowed to fall from a position where B = 0 to a new position where B = T and is the magnetic field directed perpendicular to the plane of the coil. Calculate the magnitude of the average emf that is induced in the coil if the displacement occurs in s.3. A 25-turn circular coil of wire has diameter 1.00 m. It is placed with its axis along the direction of the Earth’s magnetic field of 50.0 μT, and then in s it is flipped 180°. An average emf of what magnitude is generated in the coil?6. A magnetic field of T exists within a solenoid of 500 turns and a diameter of 10.0 cm. How rapidly (that is, within what period of time) must the field be reduced to zero, if the average induced emf within the coil during this time interval is to be 10.0 kV?
23 12. A 30-turn circular coil of radius 4. 00 cm and resistance 1 12. A 30-turn circular coil of radius 4.00 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t 0t2, where t is in seconds and B is in tesla. Calculate the induced emf in the coil at t = 5.00 s.19. An automobile has a vertical radio antenna 1.20 m long. The automobile travels at 65.0 km/h on a horizontal road where the Earth’s magnetic field is 50.0 μT directed toward the north and downward at an angle of 65.0° below the horizontal. (a) Specify the direction that the automobile should move in order to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom. (b) Calculate the magnitude of this induced emf.22. A conducting rod of length ℓ moves on two horizontal, frictionless rails, as shown in Figure P If a constant force of 1.00 N moves the bar at 2.00 m/s through a magnetic field B that is directed into the page, (a) what is the current through the 8.00-Ω resistor R? (b) What is the rate at which energy is delivered to the resistor? (c) What is the mechanical power delivered by the force Fapp?
24 Rotating Generators and Faraday’s Law For N loops of wire
25 Induced emf in a Rotating Loop The induced emf in the loop isThis is sinusoidal, with emax = NABw
28 DC GeneratorsThe DC (direct current) generator has essentially the same components as the AC generatorThe main difference is that the contacts to the rotating loop are made using a split ring called a commutator
30 32. For the situation shown in Figure P31 32. For the situation shown in Figure P31.32, the magnetic field changes with time according to the expression B = (2.00t3 – 4.00t )T, and r2 = 2R = 5.00 cm. (a) Calculate the magnitude and direction of the force exerted on an electron located at point P2 when t = 2.00 s. (b) At what time is this force equal to zero?45. A proton moves through a uniform electric field E = 50.0 j V/m and a uniform magnetic field B = (0.200i j k)T. Determine the acceleration of the proton when it has a velocity v = 200 i m/s.59. A circular loop of wire of radius r is in a uniform magnetic field, with the plane of the loop perpendicular to the direction of the field (Fig. P31.59). The magnetic field varies with time according to B(t) = a + bt, where a and b are constants. (a) Calculate the magnetic flux through the loop at t = 0. (b) Calculate the emf induced in the loop. (c) If the resistance of the loop is R, what is the induced current? (d) At what rate is energy being delivered to the resistance of the loop?
31 Induced emf and Electric Fields An electric field is created in the conductor as a result of the changing magnetic fluxEven in the absence of a conducting loop, a changing magnetic field will generate an electric field in empty spaceThis induced electric field is nonconservativeUnlike the electric field produced by stationary chargesThe emf for any closed path can be expressed as the line integral of E.ds over the path
32 General form of Faraday’s Law So the electromotive force around a closed path is:And Faraday’s Law becomes:A changing magnetic flux produces an electric field.This electric field is necessarily non-conservative.
33 E produced by changing B How about outside ro ?
34 Maxwell’s EquationsThe two Gauss’s laws are symmetrical, apart from the absence of the term for magnetic monopoles in Gauss’s law for magnetismFaraday’s law and the Ampere-Maxwell law are symmetrical in that the line integrals of E and B around a closed path are related to the rate of change of the respective fluxes
35 Gauss’s law (electrical): The total electric flux through any closed surface equals the net charge inside that surface divided by eoThis relates an electric field to the charge distribution that creates itGauss’s law (magnetism):The total magnetic flux through any closed surface is zeroThis says the number of field lines that enter a closed volume must equal the number that leave that volumeThis implies the magnetic field lines cannot begin or end at any pointIsolated magnetic monopoles have not been observed in nature
36 Faraday’s law of Induction: This describes the creation of an electric field by a changing magnetic fluxThe law states that the emf, which is the line integral of the electric field around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that pathOne consequence is the current induced in a conducting loop placed in a time-varying BThe Ampere-Maxwell law is a generalization of Ampere’s lawIt describes the creation of a magnetic field by an electric field and electric currentsThe line integral of the magnetic field around any closed path is the given sum
37 The Lorentz Force LawOnce the electric and magnetic fields are known at some point in space, the force acting on a particle of charge q can be calculatedF = qE + qv x BThis relationship is called the Lorentz force lawMaxwell’s equations, together with this force law, completely describe all classical electromagnetic interactions