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9.3 Motors and generators: 1. Motors and magnetic forces

Syllabus reference (October 2002 version)
1. Motors use the effect of forces on current-carrying conductors in magnetic fields	Students learn to: discuss the effect on the magnitude of the force on a current-carrying conductor of variations in: the strength of the magnetic field in which it is located the magnitude of the current in the conductor the length of the conductor in the external magnetic field the angle between the direction of the external magnetic field and the direction of the length of the conductor describe qualitatively and quantitatively the force between long parallel current-carrying conductors: define torque as the turning moment of a force using: identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces describe the main features of a DC electric motor and the role of each feature identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets	Students: solve problems using: perform a first-hand investigation to demonstrate the motor effect solve problems and analyse information about the force on current-carrying conductors in magnetic fields using: F=B I l sinθ solve problems and analyse information about simple motors using: identify data sources, gather and process information to qualitatively describe the application of the motor effect in: the galvanometer the loudspeaker

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 18 Sep 03]

Prior learning: Preliminary module 8.3.

Background: Moving charged particles are deflected by a magnetic field. Since the particles have mass, there must be a force to cause the change of direction. The force acts only while a charged particle is moving within a magnetic field.

Electric current in a conductor consists of a flow of charged particles, electrons, moving with a net velocity. When these particles move through a magnetic field, they experience a force, but are constrained by being inside the conductor. The force is therefore transferred to the conductor, causing it to move relative to the external magnetic field.

An electric motor is a device that transforms electrical energy into mechanical energy by using the motor effect.

For interest: Thomas Davenport built the first working electric motor in 1833. His design was successful because he used a commutator and brushes. (The American Society of Mechanical Engineers)

perform a first-hand investigation to demonstrate the motor effect

• You should perform a first-hand investigation to make the motor effect happen by carrying out a planned procedure, recognising where and when modifications to the materials and structures are needed and analysing the effect of these adjustments. Your teacher may plan an investigation for you or you may choose one similar to the following procedure.

identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field

• The force on a current-carrying conductor in a magnetic field causes the conductor to move relative to the magnetic field. This movement is referred to as the motor effect.

discuss the effect on the magnitude of the force on a current-carrying conductor of variations in:

• the strength of the magnetic field in which it is located
• the magnitude of the current in the conductor
• the length of the conductor in the external magnetic field
• the angle between the direction of the external magnetic field and the direction of the length of the conductor

• The force on a charged particle moving in a magnetic field is proportional to the strength of the magnetic field. Therefore, the stronger the magnetic field, the greater the force on a current-carrying conductor in the magnetic field and vice versa.
  
  
• Increasing the potential difference across a conductor increases the drift velocity of electrons within the conductor, thus increasing the current in proportion. Each moving charged particle experiences a force due to the magnetic field in proportion to its velocity. Therefore, the magnitude of the force on a current-carrying conductor varies in proportion to the magnitude of the current in the conductor.
  
  
• The longer the section of current-carrying conductor in a magnetic field, the more moving electrons simultaneously experience a force due to the field. Therefore, the magnitude of the force on a current-carrying conductor varies in proportion to the length of the conductor in the magnetic field.
  
  
• The force on a charged particle moving in a magnetic field is at its maximum when the particle is moving at right angles to the direction of the magnetic field and zero when the particle is moving parallel to the field. The direction of the drift velocity of electrons in a conductor is along the length of the conductor. Thus, the magnitude of the force on a current-carrying conductor in a magnetic field varies with the angle between the direction of the length of the conductor and the direction of the magnetic field. The force is at a maximum when the angle between the conductor and the magnetic field is 90° and zero when the conductor lies parallel to the field.

solve problems and analyse information about the force on current-carrying conductors in magnetic fields using

• You are required to perform numerical calculations using the formula . You will need to select from different strategies which could be used to solve the problem. This could include rearranging the equation if necessary to have the required variable as the subject of the equation, then substituting known values of variables into the equation to calculate the value of the required variable.
  
  Note that when the current-carrying conductor is at right angles to the direction of the magnetic field, sin θ = 1.0 and the equation reduces to F = BIl. When the current-carrying conductor is parallel to the direction of the magnetic field, θ is zero, sin θ is zero and therefore F is zero.

• You must be able to analyse information about the force on current-carrying conductors in magnetic fields using the given equation. You will need to identify the relationship between the force and each other variable in turn by substituting constant values for the other three variables into the equation. You could use a graph to analyse any relationship.

describe qualitatively and quantitatively the force between long parallel current-carrying conductors:

Qualitative description:

• The force between the conductors exists because the magnetic field due to the current in each conductor interacts with the magnetic field due to the current in the other conductor. The direction of the force (attraction or repulsion) depends on the relative directions of the two currents. If the two currents are flowing in the same direction, each conductor experiences an attractive force, that is, towards the other conductor. If the currents are flowing in opposite directions, each conductor experiences a repulsive force.
  
  
• The magnitude of the force between the two conductors depends on the magnitude of the current in each wire, increasing or decreasing with the product of the two currents. The force also depends on the distance of separation between the two conductors, increasing as the conductors are brought closer together, and decreasing as they are moved apart.
  
  
• The force between the conductors depends on the length of the parallel conductors, being larger for longer conductors. We usually speak of the “force per unit length” which varies only with the magnitude of the two currents and with the distance between the conductors.

A quantitative description is provided by the equation , where:

F is the force between the conductors

I1 and I2 are the currents in the two conductors, respectively

d is the distance of separation between the conductors, and

l is the length of the parallel conductors.

• Because force is a vector quantity, the direction of the forces involved is important and must be specified.
  
  
• Force, F, between two long parallel current-carrying conductors is:
  • proportional to the product of the two currents,I1 and I2
  • inversely proportional to the separation, d, between the conductors
  • proportional to the length, l, of the parallel conductors.
  
  
• Force per unit length between two long parallel current-carrying conductors is:
  • proportional to the product of the two currents,I1 and I2
  • inversely proportional to the separation, d, between the conductors
  • independent of length.
  
  
• The k in the equation is an experimentally derived constant which has the value 2 x 10^-7 T m A^-1.

solve problems using:

• You must be able to solve numerical problems and perform calculations involving the equation given. You will need to be able to identify the nature of the problem by identifying the given data as well as the unknown variable whose value is required by the problem. You will need to be able to calculate the value of the unknown variable from values given for the other variables. This could involve changing the subject of the equation.

define torque as the turning moment of a force using:

• Torque is defined as the turning moment of a force, that is, , where:
  • τ is the torque
  • F is the component of the applied force perpendicular to the axis of rotation
  • d is the perpendicular distance from the axis to the line of action of the force.
  • The force is applied acting in a clockwise or anticlockwise direction about an axis of rotation.

describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces

The forces experienced by a current-carrying loop in a magnetic field depend on the orientation of the loop relative to the magnetic field. You will need to describe both the direction and the relative magnitude of particular forces, in addition to the net result of all forces.

Assume, for simplicity of discussion, that the axis of a rectangular coil is perpendicular to the magnetic field, and that the long sides of the coil are parallel to the axis and equidistant from it.

• Each long side of the coil experiences a force whose magnitude does not change throughout a rotation of the coil, since the sides always remain perpendicular to the field. The force on each long side can be shown, by the right-hand palm rule, to be always in the same direction throughout a rotation of the coil, opposite in direction to the force on the other long side, and always perpendicular to the axis.
  
  
• Each end of the coil will experience a force which varies from zero, when the plane of the coil is parallel to the field, to a maximum when the plane of the coil is perpendicular to the field. The forces on the two ends can be shown, by the right-hand palm rule, to be opposite in direction, always parallel to the axis, and alternating in direction through a full rotation of the coil.
  
  
• The force on each long side produces a torque about the axis. As the forces are in opposite directions, and their lines of action are on opposite sides of the axis, they produce a torque in the same direction. Thus, their effect is to rotate the coil about its axis. The net torque is at its maximum when the plane of the coil is parallel to the field, as the perpendicular distance, d, to the line of action is maximum, and reduces to zero as the plane of the coil rotates to be perpendicular to the field, as the line of action of each force is then through the axis (d = zero). The direction of the torque alternates through a complete rotation of the coil: its direction is always to rotate the coil to be perpendicular to the field.
  
  
• As the forces on the two ends are always opposite in direction, and always parallel to the axis, their net effect is zero.
  
  
• For any current-carrying loop in a magnetic field, free to rotate about any axis, the net effect of the forces will be such as to rotate the loop to lie perpendicular to the magnetic field. A current-carrying loop orientated in a plane at right angles to a magnetic field will experience no net force.

1. In this position torque is maximum and in clockwise direction. Force on the ends is zero.	2. Force on the ends is outwards.
3. In this position torque is zero. Force on the ends is maximum.	4. The torque is anti-clockwise.
5. The torque is anti-clockwise.	6. Force on the ends is inwards.

solve problems and analyse information about simple motors using

• Solve problems using the equation by selecting a strategy, such as rearranging the equation as necessary, then substituting given numerical values for known variables, so that you can calculate the value of the unknown variable. You should ensure that you can rearrange any equation successfully to change the subject of the equation to the unknown variable as required.
  
  
• Analyse information about simple motors by using the equation as a mathematical model to explain the factors involved in producing the torque. You should be able to predict the effect on the torque of changing any of the other variables.

describe the main features of a DC electric motor and the role of each feature

This dot point would be well supported by an activity involving the dismantling of a simple commercial electric motor from a child's battery-operated (DC) toy. Web sites are listed below that describe the procedure and identify the parts of the motor. If care is taken the motor can be reassembled and made functional again after the activity. Alternatively, this activity could be replaced by observation of a laboratory model DC electric motor that has all the main components exposed.

• A table is an efficient means of presenting a description of the main features or parts of a DC electric motor and the role of each feature.

Part	Description	Role of the part
For the external magnets, one of the following arrangements is used:
A. a pair of permanent magnets in a simple motor	Two permanent magnets on opposite sides of the motor, with opposite poles facing each other. The pole faces are curved to fit around the armature.	The magnets supply the magnetic field which interacts with the current in the armature to produce the motor effect. The shape of the pole faces makes the magnetic field almost uniformly radial where the coil passes.
B. pairs of electromagnetic coils in a more complex motor	Each stator coil (or “field” coil) is wound on a soft iron core attached to the casing of the motor. The coils are shaped to fit around the armature.	Each opposed pair of stator coils produces a magnetic field similar to that provided by a pair of permanent magnets. The iron core concentrates the field.
Other parts:
Armature	The armature consists of a cylinder of laminated iron mounted on an axle. Often there are longitudinal grooves into which the coils are wound.	The armature carries the rotor coils. The iron core greatly concentrates the external magnetic field, increasing the torque on the armature. The laminations reduce eddy currents which might otherwise overheat the armature.
Rotor coil(s)	There may be only one, in a very simple motor, or several coils, usually of several turns of insulated wire, wound onto the armature. The ends of the coils are connected to bars on the commutator.	The coils provide torque, as the current passing through the coils interacts with the magnetic field. As the coils are mounted firmly on the rotor, any torque acting on the coils is transferred to the rotor and thence to the axle.
Split-ring  commutator	The commutator is a broad ring of metal mounted on the axle at one end of the armature, and cut into an even number of separate bars (two in a simple motor). Each opposite pair of bars is connected to one coil.	The commutator provides points of contact between the rotor coils and the external electric circuit. It serves to reverse the direction of current flow in each coil every half-revolution of the motor. This ensures that the torque on each coil is always in the same direction.
Brushes	Compressed carbon blocks, connected to the external circuit, mounted on opposite sides of the commutator and spring-loaded to make close contact with the commutator bars.	The brushes are the fixed position electrical contacts between the external circuit and the rotor coils. Their position brings them into contact with both ends of each coil simultaneously, as each coil is positioned at right angles to the field, to maximise torque.
Axle	A cylindrical bar of hardened steel passing through the centre of the armature and the commutator.	The axle provides a centre of rotation for the moving parts of the motor. Useful work can be extracted from the motor via a pulley or cog mounted on the axle.

Inside an electric motor More Parts, HowStuffWorks.com

How electric motors work Parts of an Electric Motor, HowStuffWorks.com

How electric motors work Electromagnets and Motors, HowStuffWorks.com

Stripped down motor Exploratorium, The Museum of Science, Art and Human Perception, San Francisco, USA (As motors go,this is about as simple as it gets.)

Motor control tutorial DC motors (GIF animation of a simple DC motor) Motorola, Inc.

identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets

• The required magnetic fields in DC motors can be produced by permanent magnets shaped to fit around the armature.
  
  
• Alternatively, electromagnets can be produced by winding coils around iron cores attached to the case of the motor and passing current through these coils at the same time as through the rotor coils. These stator coils are wound so that pairs of coils facing the rotor coils have magnetic fields the same as would be produced by pairs of permanent magnets with their north and south poles facing each other.

identify data sources, gather and process information to qualitatively describe the application of the motor effect in:

• the galvanometer
• the loudspeaker

• Identify data sources by first determining the type of data that must be collected. You need to find information about galvanometers and about loudspeakers that is specifically about how the motor effect is produced and used in these devices.
  
  
• Continue by looking for such information on the Internet, in CD-ROMs and in books, including text books, popular scientific journals, technical manuals and encyclopaedia. Skim and scan the information to identify keywords in the text. Ask yourself whether the information presented is explicitly concerned with the motor effect at work in either a galvanometer or a loudspeaker, and discard sources that are irrelevant. Look for diagrams that will help your description.
  
  You should also examine a demonstration galvanometer or a partially dismantled loudspeaker, if one is available.
  
  The following web sites could be a start for you in gathering the information:
  
  Moving coil galvanometer citycollegiate.com
  
  How speakers work HowStuffWorks.com
  
  Dynamic loudspeaker principle Hyper Physics, Georgia State University, USA
  
  
• Gather information that is relevant to the required description of applications of the motor effect by summarising important sections of text and drawing diagrams as appropriate. Collate information on the same topic from different sources.
  
  
• Process the information you gather by comparing different sources to assess the reliability of the information. Use the information to compile, in your own words, a qualitative description of how the motor effect is applied in each device.