1 Current in a Magnetic Field Learning Outcomes Discuss the force on a current-carrying conductor in a magnetic field. Demonstrate this force. Solve problems about this force. Discuss applications of this force. Define magnetic flux density. Discuss the force between currents. HL: Define the ampere. HL: Derive F = qvb Solve problems about magnetic flux density. 2 Force on a Current-Carrying Conductor Recall a current-carrying conductor has a magnetic field around it. This field will interact with other nearby magnetic fields. This results in a force on the conductor. The size and direction of the force depends on the nature of the two fields. The force is always: perpendicular to the current, perpendicular to the magnetic field. 3 To Demonstrate the Force on a Current- Carrying Conductor in a Magnetic Field 1. Set up a strip of tin foil between the north and south poles of a magnet (or two magnets). 2. Note no deflection on the foil. 3. Pass a current through the foil. 4. The foil will move towards one of the poles, depending on which way the current flows. 5. The foil must be experiencing a force due to the external magnetic field. 1
4 Uses of this Force This force is the basis for a number of electronic devices: Electric motor Moving coil loudspeaker Various moving coil meters (voltmeter, ammeter etc.) The jist is these devices respond to the size of the current being passed through them. More detail on these in the applied electricity option (we probably won t do this). 5 Fleming s Left-Hand Rule If the thumb, index finger, and middle finger of the left hand are held at right angles to each other; with the index finger pointing in the direction of the magnetic field and middle finger pointing in the direction of the current, the thumb will point in the direction of the force. 6 Fleming s Left-Hand Rule e.g. the diagram shows a current-carrying wire in a magnetic field. In which direction is the force on the wire? 2
7 Magnetic Flux Density The strength of a magnetic field is given by its magnetic flux density. The magnetic flux density, B at a point in a magnetic field is a vector whose magnitude is equal to the force per unit current per unit length that would be experienced by a conductor at right angles to the field at that point and whose direction is the direction of the force on a north pole placed at that point. Formula: B = F Il B = magnetic flux density, F = force, I = current, l = length. 8 Magnetic Flux Density The unit of magnetic flux density is the tesla, T. The magnetic flux density at a point is 1 tesla if a conductor of length 1 m carrying a current of 1 A experiences a force of 1 N when placed perpendicular to the field. 9 Force on a Current-Carrying Conductor Rearranging this formula gives: F = BIl This tells us the force is: proportional to the magnetic flux density, proportional to the current, proportional to the length of the conductor. 3
10 Force on a Current-Carrying Conductor e.g. A straight piece of wire of length 3 m carrying a current of 2 A experiences a force of 12 N when placed perpendicular to a uniform magnetic field. Calculate the value of the magnetic flux density. e.g. A straight piece of wire carrying a current of 4 A is placed at an angle of 30 o to a magnetic field of flux density 2 T. The wire is 2 m long. What is the magnitude and direction of the force on the wire? 11 Force on a Current-Carrying Conductor e.g. The loop shown is free to rotate about its axis. i. Find the magnitude and direction of the force acting on each part of the loop. ii. iii. Find the moment of the force about the axis. What happens to the moment as the loop rotates? 12 D.C. Motors Consider a loop that is free to rotate in a magnetic field. What is the direction of force on each part of the loop? What is the effect on the loop? 4
13 D.C. Motors 14 D.C. Motors 15 Force Between Wires The force experienced by these wires is: A. both left B. both right C. attractive D. repulsive 5
16 Force Between Wires The force experienced by these wires is: A. both left B. both right C. attractive D. repulsive 17 The Ampere From this force between wires, we get the definition of the ampere: The ampere is that constant current, which, if maintained between two straight, parallel conductors of infinite length and negligible cross-section, kept 1 metre apart in a vacuum will exert a force of 2 10 7 newtons per metre length of the other. As the ampere is a fundamental SI unit, we define the coulomb based on it: The coulomb is the amount of charge that passes any point in a circuit when a current of 1 ampere flows for 1 second. 18 Just as current-carrying wires generate a magnetic field and are affected by external fields, charges moving without a wire will also exhibit this. e.g. cathode rays, thermionic emissions, photoelectric emissions, ions in electrolyte solutions. We will look at each of these devices in turn in other sections of the course. 6
19 What direction is the force on this stream of electrons? 20 Derive: F = qvb Consider a current-carrying conductor of length l with current I. The flowing charges are size q and have velocity v. 21 I = q (by definition) t v = l l = vt t Substituting into F = BIl gives: F = B q vt = qvb t 7
22 Consider an electron moving with velocity v in a magnetic field. In what direction is the force on the electron? 23 Force on Charge in a Magnetic Field e.g. A charge of 2 C moves at a speed of 10 m s -1 at right angles to a magnetic field of flux density 2 T. What is the force on the charge? e.g. An electron of charge 1.6 10-19 C enters a uniform magnetic field of flux density 2 T and moves at right angles to the field. If the force on the electron is 2 10-8 N, calculate the speed of the electron. e.g. Prove that the period T of the circular orbit of an electron of mass m and charge e when moving at speed v perpendicular to a magnetic field of flux density B is given by: T = 2πm Be 8