Application Of Faraday s Law Dr Miguel Cavero September 2, 2014 Application Of Faraday s Law September 2, 2014 1 / 23
The PHYS120 Exam will be divided into three sections as follows: Section A: Short Questions (20 3-mark questions) 10 Electricity and Magnetism questions 5 Optics questions 5 Atomic and Nuclear Physics questions Section B: Electricity and Magnetism (60 marks) Section B: Optics and Atomic and Nuclear Physics (60 marks) Application Of Faraday s Law PHYS120 Exam September 2, 2014 3 / 23
Faraday s Law The induced emf around a closed path is the negative of the rate of change of the magnetic flux: E = dφ B dt where the magnetic fulx φ B is (B cos θ)a, the component of the magnetic field B perpendicular to the area A multiplied by the area. The negative sign means that the induced emf E opposes the change in the magnetic flux φ B. Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 5 / 23
Changing Magnetic Flux And An Induced Emf A wire is shaped so that it forms a square coil with 25 turns. Each side of the square has a length of 1.80 cm. The coil is placed in the xz-plane, in the presence of a magnetic field B which is directed perpendicular to the plane of the coil (i.e. in the y-direction). If the magnetic field changes uniformly from 0 T to 0.500 T in a time of 0.800 s, calculate the induced emf in the coil while the field is changing? Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 6 / 23
Changing Magnetic Flux And An Induced Emf Faraday s Law states that E = dφ B dt If a coil/loop contains N turns and the magnetic flux changes uniformly, then the induced emf can be written as E = N φ B t Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 7 / 23
Changing Magnetic Flux And An Induced Emf Calculate the magnetic flux, by first finding the area of the coil. The side of the square is 1.80 cm, therefore the area is A = (1.80 10 2 ) 2 = 32.4 10 4 m To find the change in the magnetic flux, calculate the initial and final flux. Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 8 / 23
Changing Magnetic Flux And An Induced Emf The initial and final magnetic flux values are φ I B = (BI cos θ)a = 0 φ F B = (BF cos θ)a = (0.500) (32.4 10 4 ) = 1.62 10 4 Wb Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 9 / 23
Changing Magnetic Flux And An Induced Emf The change in the magnetic flux in a time of 0.800 s is φ B t = 1.62 10 4 0 0.0800 Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 10 / 23
Changing Magnetic Flux And An Induced Emf The induced emf is therefore E = N φ B t 1.62 10 4 = (25) 0.0800 = 5.06 10 3 V Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 11 / 23
Changing Magnetic Flux And An Induced Emf Let the resistance of the coil be 0.350 Ω. What is the induced current in the coil? Using Ohm s Law, the current in the coil is I = E R = 5.06 10 3 0.350 What is the direction of this current? = 1.45 10 2 A Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 12 / 23
Lenz s Law The negative sign in Faraday s Law indicates the polarity of the induced emf. To determine in which direction the current will flow in the loop, Lenz s Law is used. Lenz s Law states that the current caused be the induced magnetic field travels in the direction that creates a magnetic field with a flux opposing the change in the original flux. If the magnetic flux through the loop becomes more positive, the induced emf produces a current and hence a magnetic field that produces a negative magnetic flux. Note that the induced magnetic field does not always point in the opposite direction to the applied magnetic field. Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 13 / 23
Changing Magnetic Flux And An Induced Emf The magnetic field B is increasing (from 0 T to 0.500 T) in the positive y-direction. The flux therefore is positive and increasing in that direction. The induced magnetic field points in the y-direction, creating a magnetic flux that opposes the change. Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 14 / 23
Changing Magnetic Flux And An Induced Emf Using the second right-hand rule for the induced magnetic field, the fingers curl down through the coil when the thumb points in a clockwise direction. The induced current I therefore flows in the clockwise direction in this coil. Application Of Faraday s Law Application Of Faraday s Law September 2, 2014 15 / 23
AC Generator Generators and motors operate on the principle of electromagnetic induction. An alternating-current (AC) generator converts mechanical energy into electrical energy. The generator is essentially a coil of many turns that is made to rotate in the presence of a magnetic field. The energy required to rotate the coil comes from an outside source (e.g. falling water in a hydroelectric power plant). A rotating coil results in a changing magnetic flux and therefore induced a current in the coil. Application Of Faraday s Law Generators And Transformers September 2, 2014 17 / 23
AC Generator Let a coil have N turns and an area A, and rotate with an angular velocity ω. If the normal of the coil makes an initial angle α to the magnetic field, then the angle θ between the normal and the magnetic field at a time t is given by θ = α + ωt Application Of Faraday s Law Generators And Transformers September 2, 2014 18 / 23
AC Generator The induced emf is then E = N d [AB cos(α + ωt)] dt = (NABω) sin(α + ωt) Application Of Faraday s Law Generators And Transformers September 2, 2014 19 / 23
DC Generator A direct-current (DC) generator works in the same way as an AC generator, except that the rotating coil is connected to an external circuit by means of a split ring called a commutator. The commutator always ensures that the induced emf always has the same polarity, giving rise to a direct current. Application Of Faraday s Law Generators And Transformers September 2, 2014 20 / 23
Transformers A transformer is made of two coils wrapped around an iron core. An alternating emf source E 1 is applied to one of the coils (the primary) which has N 1 turns. Application Of Faraday s Law Generators And Transformers September 2, 2014 21 / 23
Transformers The current I 1 due to E 1 creates a changing magnetic field inside the iron core, which gives rise to a changing flux the secondary coil (with N 2 turns in it). By Faraday s Law, an alternating emf E 2 is induced in the secondary coil, producing a current I 2 in it. Application Of Faraday s Law Generators And Transformers September 2, 2014 22 / 23
Transformers It can be shown that E 2 E 1 = N 2 N 1 = I 1 I 2 If N 2 > N 1, the transformer is a step-up transformer (since E 2 > E 1 ). If N 2 < N 1, the transformer is a step-down transformer (since E 2 < E 1 ). Application Of Faraday s Law Generators And Transformers September 2, 2014 23 / 23