Teaching Aid: Measuring the Strength of a Magnetic Field PowerPoint
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Measuring the strength of a Magnetic Field © David Hoult 2009 When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is © David Hoult 2009 When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines © David Hoult 2009 When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines © David Hoult 2009 When current flows through a conductor which is in a magnetic field, it experiences a force, except when the conductor is parallel to the flux lines The direction of the force is at 90° to both the current and the flux lines Fleming’s left hand rule helps to remember the relation between the three directions… © David Hoult 2009 © David Hoult 2009 © David Hoult 2009 Thumb First finger Second finger © David Hoult 2009 ThuMb Motion First finger Second finger © David Hoult 2009 ThuMb Motion First finger Field Second finger © David Hoult 2009 ThuMb Motion First finger Field SeCond finger Current © David Hoult 2009 © David Hoult 2009 © David Hoult 2009 © David Hoult 2009 © David Hoult 2009 Factors affecting the Magnitude of the Force The force depends on © David Hoult 2009 The force depends on - the current flowing through the conductor, I © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F a current, I © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F a current, I F a length of conductor, L © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F a current, I F a length of conductor, L F = I L × a constant © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F a current, I F a length of conductor, L F = I L × a constant magnetic field strength or © David Hoult 2009 The force depends on - the current flowing through the conductor - the length of conductor in the field Experiments show that F a current, I F a length of conductor, L F = I L × a constant magnetic field strength or magnetic flux density © David Hoult 2009 F = ILB © David Hoult 2009 F = ILB units of B Newtons per Amp per meter, NA-1m-1 © David Hoult 2009 F = ILB units of B Newtons per Amp per meter, NA-1m-1 1 NA-1m-1 is called 1 Tesla (1 T) © David Hoult 2009 F = ILB units of B Newtons per Amp per meter NA-1m-1 1 NA-1m-1 is called 1 Tesla (1 T) The flux density of a magnetic field is © David Hoult 2009 F = ILB units of B Newtons per Amp per meter NA-1m-1 1 NA-1m-1 is called 1 Tesla (1 T) The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field © David Hoult 2009 F = ILB units of B Newtons per Amp per meter NA-1m-1 1 NA-1m-1 is called 1 Tesla (1 T) The flux density of a magnetic field is the force per unit current per unit length acting on a conductor placed at 90° to the field F = I L B sin q © David Hoult 2009 Force acting on a charged particle moving through a magnetic field © David Hoult 2009 © David Hoult 2009 Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009 Consider a conductor of length L, having n free electrons per unit volume. A current, I, is flowing through it © David Hoult 2009 In this piece of conductor there are © David Hoult 2009 In this piece of conductor there are NAL free electrons © David Hoult 2009 In this piece of conductor there are NAL free electrons If all these electrons pass through end x in time t then the current, I is given by © David Hoult 2009 In this piece of conductor there are NAL free electrons If all these electrons pass through end x in time t then the current, I is given by nALe t © David Hoult 2009 If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude © David Hoult 2009 If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B © David Hoult 2009 If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by © David Hoult 2009 If there is a magnetic field of flux density B at 90° to the current, the conductor will experience a force of magnitude I L B This is the sum of the forces on all the electrons, so the force F acting on each electron is given by F = ILB = IB nA nAL © David Hoult 2009 Substituting for I gives F = © David Hoult 2009 Substituting for I gives nALeB F = tnA = © David Hoult 2009 Substituting for I gives nALeB F = tnA = LeB t © David Hoult 2009 Substituting for I gives nALeB F = tnA = LeB t © David Hoult 2009 but L/t is © David Hoult 2009 but L/t is the (drift) velocity of the electrons © David Hoult 2009 but L/t is the (drift) velocity of the electrons therefore © David Hoult 2009 but L/t is the (drift) velocity of the electrons therefore F =evB © David Hoult 2009 In general the magnitude of the force acting on a charged particle moving with velocity v, at 90° to a magnetic field of flux density B, is given by F = qvB where q is the charge on the particle © David Hoult 2009 If the particle moves at angle q to the field © David Hoult 2009 If the particle moves at angle q to the field the magnitude of the component of its velocity at 90° to the field is © David Hoult 2009 If the particle moves at angle q to the field the magnitude of the component of its velocity at 90° to the field is v cos a © David Hoult 2009 If the particle moves at angle q to the field the magnitude of the component of its velocity at 90° to the field is v cos a = v sin q Therefore, in general F = © David Hoult 2009 If the particle moves at angle q to the field the magnitude of the component of its velocity at 90° to the field is v cos a = v sin q Therefore, in general F = q v B sin q © David Hoult 2009 The Motion of Charged Particles in Magnetic Fields © David Hoult 2009 A charged particle moving parallel to the flux lines © David Hoult 2009 A charged particle moving parallel to the flux lines experiences no force © David Hoult 2009 A charged particle moving parallel to the flux lines experiences no force There are three possible paths for a charged particle moving through a uniform magnetic field © David Hoult 2009 If the angle, q between the field and the direction of motion is zero the path is © David Hoult 2009 If the angle, q between the field and the direction of motion is zero the path is a straight line © David Hoult 2009 If the angle, q between the field and the direction of motion is 90° the path is © David Hoult 2009 If the angle, q between the field and the direction of motion is 90° the path is circular field into plane of diagram © David Hoult 2009 If the angle, q between the field and the direction of motion is 90° the path is circular field into plane of diagram © David Hoult 2009 If the angle, q between the field and the direction of motion is 90° the path is circular field into plane of diagram © David Hoult 2009 If the angle between the field and the direction of motion is 0° < q < 90° the path is © David Hoult 2009 If the angle between the field and the direction of motion is 0° < q < 90° the path is © David Hoult 2009 If the angle between the field and the direction of motion is 0° < q < 90° the path is © David Hoult 2009 If the angle between the field and the direction of motion is 0° < q < 90° the path is a helix © David Hoult 2009
