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Transcript
AQA A2 Physics A Unit 4 Magnetic Fields D Ewart Magnetic Fields Lessons Topics 1 Magnetic flux density Force on a current-carrying wire in a magnetic field. F = B I l, when field is perpendicular to current. Fleming’s left hand rule. Magnetic flux density B and definition of the tesla 2 to 3 Moving charges in a magnetic field Force on charged particles moving in a magnetic field. F = B Q v when the field is perpendicular to velocity. Circular path of particles; application in devices such as the cyclotron. 4 to 5 Magnetic flux and flux linkage Magnetic flux defined by Φ = B A with B normal to A. Flux linkage as NΦ where N is the number of turns cutting the flux. Flux and flux linkage passing through a rectangular coil rotated in a magnetic field: flux linkage NΦ = BAN cosθ where θ is the angle between the normal to the plane of the coil and the magnetic field. Current Carrying Conductors in a Magnetic Field Magnetic field revision The way that we refer to poles and the Earth’s magnetism leaves a lot of room for confusion as I’m sure you remember from year 8. -1- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart A magnetic field is _________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ ______________________________________________(see page 106) We always draw the field lines running from north to south, and we say that these lines of forces (magnetic field lines) are lines along which a free north pole would move. What causes the Earth’s magnetic field? ______________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Force on a current in a magnetic field When a current carrying wire (moving charges) is in a field it experiences a force, as long as it isn’t in line with the field lines. It will be at a maximum when at 900 to the field line. We use Fleming’s left hand rule to remember how the forces direction is related to the current and field. -2- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart This is called the motor effect and is a result of the interaction of the two fields. The strength of a magnetic field is usually measured in terms of a quantity called the magnetic flux density of the field, B. A definition of B requires a consideration of the forces produced by electromagnetic fields. As we have already mentioned when a wire carrying a current is placed in a magnetic field the wire experiences a force due to the interaction between the field and the moving charges in the wire. A very good demonstration is the so-called catapult field experiment in which a wire carrying a d.c. current can be made to move in the field of two flat magnets. Before considering the mathematical nature of the forces on currents in magnetic fields it is worth just looking at the simple magnetic field diagrams that give rise to these effects. These are shown in Figure 1. (a) is the field between two magnets, (b) the field due to a current in a straight wire and (c) the resulting field if they are put together. This last field is known as the “catapult” field because it tends to catapult the wire out of the field in the direction shown by the arrow. Fig 1 The force F on the wire in Figure 1 (c) can be shown to be proportional to (a) the current on the wire I, (b) the length of the conductor in the field L, (c) the sine of the angle that the conductor makes with the field q, and (d) the strength of the field - this is measured by a quantity known as the magnetic flux density B of the field. The force is given by the equation: Force on current in magnetic field: F = BIL sin θ If we keep things simple and consider the current at 900 to the field then the formula is: F = BIL -3- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart The units for B are tesla (T) which is equal to _________________________________ The flux density of a field of one tesla is therefore defined as the force per unit length on a wire carrying a current of one ampere at right angles to the field. -4- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart Coils and Couples If a coil carrying a current is placed in a magnetic field it will experience a force on two of its sides in such a way as to make the coil rotate. This effect is the basis of all electric motors and moving coil meters. Think of all the places where electric motors are used from stereos, disc drives, CD players, starter motors in cars, washing machines etc. etc. and you will realise how important this effect is! The forces are shown below. If we coil wire together we can increase this force and with current running in opposite directions we can create a “couple” – this is a very basic motor. The d.c motor consists of: (a) a number of coils of fine wire wound on (b) a laminated soft iron armature (c) a set of brushes to allow current to enter and leave the windings; (d) a commutator to reverse the current in the coils; (e) a set of external field coils. If we start with the coil in the position shown in diagram Figure 2(a) then there will be an upward force on side (1) of the coil and a downward force on side (2) of the coil. The coil will therefore start to twist in an anticlockwise direction. The inertia of the coil and core keeps it turning until the input wires make contact with the ends of the coil again. This time the positive wire touches side (2) and the negative wire touches side (1). (Figure 2(b)). Side (2) now moves up and side (1) moves down — the coil continues to turn in an anticlockwise direction. This process then continues and so the coil spins. Complete summary question on page 109 -5- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart Moving Charges in a Magnetic Field Electric current in a wire is caused by the flow of negatively charged electrons. These charged particles are affected by magnetic fields – so a current- carrying wire moves in a magnetic field. 1. The equation for the force exerted on a current-carrying wire in a magnetic field perpendicular to the current is: Equation 1: 2. To see how this relates to the charged particles moving through a wire, you need to know that electric current, I, is the flow of charge, Q, per unit time, t. 3. A charged particle which moves a distance l in a time t has a velocity, v: 4. So, putting the two equations together gives the current in terms of the charge flowing through the wire: Equation 2: -6- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart If the direction of motion of a charged particle in a magnetic field is at angle θ to the lines of the field, then the component of B perpendicular to the direction of motion of the charged particle, Bsin θ, is used to give F= BQvsin θ If the velocity of the charged particle is perpendicular to the direction of the magnetic field, θ = 90o so the equation becomes If the velocity of the charged particle is parallel to the direction of the magnetic field, θ = 0o so F = Example What is the force acting on an electron travelling at 2 x 104ms-1 through a uniform magnetic field of strength 2T? (The magnitude of the charge on an electron is 1.6 x 10-19C) Explain what a Hall Probe is. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Complete questions 1 +2 page 112 -7- AQA A2 Physics A Unit 4 Magnetic Fields D Ewart The Movement of Charged Particles in Magnetic Fields Sketch a diagram of an electron moving in a uniform magnetic field of flux density B. The electron of charge e, enters the field with a velocity v. The electron experiences a force at right angles to both the field and to its instantaneous velocity. Use Fleming’s Left Hand Rule to judge the direction of the force The electron experiences no acceleration in the direction of its existing velocity as the force is at right angles to this direction. The electron does experience an acceleration at right angles to its existing velocity. When the electron has changed direction, the direction of the force that it experiences will also change: the force will always be at right angles to its current velocity. The magnitude of the new force is the same as the old force since the electron has not changed its speed. In other words, the electron will travel in a circular path. The centripetal force that causes the circular motion is F The radius, r, of the circular path can be found by equating the expressions for centripetal force and for the force on a moving charge in a magnetic field: Where m is the electron’s mass. Rearranging this equation gives: -8- AQA A2 Physics A Unit 4 Magnetic Fields The cyclotron (pg113 &114) Using a diagram explain how a Cyclotron Works Using a diagram explain how a Mass Spectrometer Works Complete questions 1 – 4 page 115 -9- D Ewart