F. Electricity and Magnetism · Electricity and MagnetismThe Motor Principle and the DC Motor
F3.4 F3.5 F3.6 F3.2 F3.3About 75 minutes
Learning goals- I can state the motor principle and explain it as an interaction of two magnetic fields.
- I can use the right-hand rule for motors (and the left-hand version for electron flow) to find the direction of the force on a conductor.
- I can name the parts of a DC motor and explain the job of each, especially the split-ring commutator.
- I can explain how a loudspeaker and an analog meter use the motor principle.
Words to know
motor principle
A current-carrying conductor in an external magnetic field experiences a force perpendicular to both the field and the current.
right-hand rule #3 (motor rule)
Open right hand: thumb along the conventional current, fingers along the external field (N to S); the palm pushes in the direction of the force.
armature
The rotating coil (usually wound on an iron core) in a motor or generator.
field magnet
The permanent magnet or electromagnet that supplies the external field in a motor.
split-ring commutator
A ring cut into two halves, attached to the armature, that reverses the current in the coil every half-turn.
brushes
Sliding contacts, often carbon, that press against the commutator and carry current into and out of the turning coil.
torque
The turning effect of a force.
Electricity that moves things
A typical home has dozens of electric motors: in the furnace fan, the fridge, the washing machine, the blender, the hair dryer, a cordless drill and, if you have one, an electric car. They all run on one idea, the motor principle. In the last lesson, a current made a magnetic field. Now we put that current in another magnetic field and watch the two fields push on each other.
The motor principle
A conductor carrying a current in an external magnetic field experiences a force. The force is perpendicular to both the current and the field.
- The force is greatest when the current is perpendicular to the field.
- There is no force when the current is parallel to the field.
- The force gets bigger with more current, a stronger field and a longer length of wire in the field.
- Reversing either the current or the field reverses the force. Reversing both leaves it unchanged.
Why it happens: two fields interacting
The wire has its own circular field (Oersted). On one side of the wire, the wire's field points the same way as the external field, so they add and the field is strong. On the other side, they point opposite ways and partly cancel, so the field is weak. The conductor is pushed from the strong-field side toward the weak-field side, like a stone in a stretched slingshot. This is sometimes called the "catapult field".
Right-hand rule #3 (the motor rule)
Hold your right hand flat and open.
- Thumb: direction of the conventional current.
- Straight fingers: direction of the external magnetic field (from N to S).
- Palm: pushes in the direction of the force on the conductor.
With electron flow, use the same rule with your left hand (thumb along the electron flow). You get the same force, because both the charge and the hand are reversed.
Check with the picture above: thumb into the page (current), fingers to the right (N to S): your palm faces down. ✓
Worked exampleExample 1: Using the motor rule
A horizontal wire runs west to east across a table, carrying conventional current east. A magnet's field points horizontally north. What is the direction of the force on the wire?
- Right hand: thumb east (current), fingers north (field).
- Your palm faces up, so the force is upward.
- Both the current and the field are horizontal and perpendicular, so the force has its largest possible size and points straight up, perpendicular to both.
Worked exampleExample 2: A page diagram
On a page, the magnetic field points into the page (×) everywhere, and a wire carries conventional current to the right. Find the force. Then check by using electron flow and the left hand.
- Right hand: thumb to the right, fingers into the page. Your palm faces up the page. Force: up the page.
- Electron flow is to the left. Left hand: thumb left, fingers into the page: the left palm also faces up the page ✓.
The DC motor
Put a rectangular coil (the armature) on an axle between the poles of a field magnet. Send a current through the coil.
- The two long sides of the coil carry current in opposite directions (one goes in, the other comes back out).
- By the motor principle, the forces on them are in opposite directions: one side is pushed up, the other down.
- This pair of forces creates a torque that turns the coil.
There is a problem. After half a turn, the sides have swapped places. If the current stayed the same, the forces would now turn the coil back, and it would just rock to a stop. The fix is the split-ring commutator: two half-rings attached to the coil, touching two fixed brushes connected to the battery. Every half-turn, each half-ring slides from one brush to the other, which reverses the current in the coil. The torque then keeps turning the coil the same way.
The coil's own momentum carries it across the gap in the commutator. Real motors have many coils at different angles and an iron core, so the torque is large and smooth.
| Part | Job |
|---|
| field magnet | provides the external magnetic field (permanent magnet or electromagnet) |
| armature (coil on iron core) | carries current; the forces on it make the torque; the iron core strengthens the field |
| split-ring commutator | reverses the current in the coil every half-turn so rotation continues in one direction |
| brushes | sliding contacts that connect the turning commutator to the stationary power supply |
| axle | turns with the armature and delivers the mechanical energy to the fan, wheel or pump |
More motor-principle devices
- Loudspeaker: a light coil, attached to a paper or plastic cone, sits in the field of a permanent magnet. The audio signal is an alternating current that changes direction and size many times a second, so the force on the coil pushes the cone back and forth in step with it. The cone pushes the air and makes sound.
- Analog ammeter (galvanometer): a coil on a pivot sits between magnet poles, held by a small spiral spring. Current makes the coil turn until the spring balances it. A larger current gives a larger turning force and a bigger needle deflection.
Looking ahead: in Grade 12 Physics (SPH4U) you will calculate the size of the force: F = BIL sin θ, where L is the length of wire in the field and θ is the angle between the wire and the field.
Just for funEvery time your phone buzzes, a tiny electric motor spins a lopsided weight (or a tiny linear motor shakes a mass back and forth) so the whole phone wobbles. Your phone is, quite literally, shaking for attention.
Hands-on activityModel a DC motor with cardboard
You need: a piece of cardboard about 10 cm × 6 cm, a pencil to act as the axle, tape, two strips of aluminium foil, two markers or crayons of different colours (or a pencil and a pen), and scissors (grown-up note: take care with scissors).
- The cardboard is your coil. Label its long edges side A and side B. Push the pencil through the middle of the short edges so the card can spin.
- Wrap two foil strips around the pencil at one end, leaving two small gaps: this is your split-ring commutator. Mark one half-ring "A" and the other "B".
- Hold two fingers against opposite sides of the foil ring: these are the brushes. Call the left finger + and the right finger −.
- Set the coil horizontal. Imagine a magnet with N on your left and S on your right. Decide which way the current goes in side A and side B, and use RHR #3 to find the force on each side. Turn the coil a quarter turn the way the forces push.
- Keep turning in quarter-turns. Each time a half-ring passes from one finger to the other, swap the current directions. Check that the forces keep turning the coil the same way.
What to look for: without the swap, after half a turn the forces would push the coil backwards. With the commutator, the side nearest the N pole always has current in the same direction, so the torque is always in the same sense. At the vertical position the forces point along the coil and give no torque; momentum carries it past.
Your turn
1State the motor principle.
A conductor carrying a current in an external magnetic field experiences a force perpendicular to both the current and the field.
2Conventional current flows north in a horizontal wire. The field points horizontally east. What is the direction of the force?
Right hand: thumb north, fingers east: palm faces down. Force: downward.
3A wire carries current parallel to a magnetic field. What is the force on it?
Zero. There is no force when the current is parallel to the field.
4The field points into the page and conventional current in a wire flows to the right. What is the force?
Thumb right, fingers into the page: palm faces up the page.
5What is the job of the split-ring commutator in a DC motor?
It reverses the current in the coil every half-turn, so the forces keep turning the coil in the same direction.
6Name four parts of a simple DC motor.
Any four: field magnet, armature (coil), split-ring commutator, brushes, axle.
7Give two ways to make a DC motor spin in the opposite direction.
Reverse the current (turn the battery around) or reverse the magnetic field (swap the magnet's poles). Doing both keeps the same direction.
More practice: warm-up
1In RHR #3, what do the thumb, fingers and palm stand for?
Thumb: conventional current; fingers: external field (N to S); palm: force.
2Which hand should you use for the motor rule if you are using electron flow?
3At what angle between the wire and the field is the force greatest?
4What do the brushes in a DC motor do?
They are sliding contacts that carry current from the stationary supply to the turning commutator.
5What energy change happens in a loudspeaker?
Electrical energy → kinetic energy of the cone → sound energy.
More practice: on your own
1Electrons flow to the left in a wire. The field points up the page. Find the force on the wire.
Conventional current is to the right. Right hand: thumb right, fingers up the page: palm faces out of the page. (Left hand with electrons to the left gives the same answer.)
2Use the idea of interacting fields to explain the direction of the force in the last question.
The wire's own circular field points down the page just in front of the page and up the page just behind it. Behind the page it adds to the upward external field (strong); in front it partly cancels it (weak). The wire is pushed from the strong side toward the weak side: out of the page, matching the hand rule.
3Why can a simple one-coil motor sometimes stop and refuse to start when the coil is vertical?
In the vertical position the forces on the sides point along the plane of the coil, so they produce no torque, and the brushes may sit on the commutator's gaps. It needs a push. Real motors use several coils at different angles so there is always torque.
4List three ways to make a DC motor produce more torque.
Any three: more current, more turns on the coil, a stronger field magnet (or electromagnet), an iron core in the armature, a larger coil.
5Explain how a loudspeaker uses the motor principle to make sound.
The speaker's coil sits in a permanent magnet's field and is attached to a cone. The audio signal is an alternating current, so the force on the coil (motor principle) reverses many times a second, pushing the cone in and out. The vibrating cone makes pressure waves in the air: sound. Larger currents give larger vibrations (louder sound).
Challenge
1(Preview of SPH4U) A 0.20 m length of wire carries 4.0 A at 90° to a 0.25 T field. Use F = BIL sin θ to find the force. What would the force be if the wire made a 30° angle with the field?
At 90°: F = (0.25)(4.0)(0.20)(sin 90°) = 0.20 N. At 30°: F = (0.25)(4.0)(0.20)(sin 30°) = 0.20 × 0.5 = 0.10 N.
2A horizontal wire 0.10 m long with a mass of 5.0 g runs east–west in a horizontal 0.50 T field that points north. (Preview of SPH4U) What current, and in which direction, would make the magnetic force hold the wire up against gravity? Use g = 9.8 N/kg.
Weight: F = mg = (0.0050)(9.8) = 0.049 N. Need BIL = 0.049: I = 0.049 ÷ (0.50 × 0.10) = 0.98 A. Direction: the force must be up. Right hand with fingers north and palm up: thumb points east. So conventional current must flow east.
3An analog ammeter's needle moves twice as far when the current doubles. Use the motor principle to explain why, and explain the job of the spring.
The turning force on the coil is proportional to the current (motor principle). The spring provides an opposing torque that increases with the angle turned. The coil stops where the two balance, so doubling the current doubles the needle's angle. Without the spring, any current would spin the coil all the way round.
Quiz
1. Which statement is the motor principle?
2. In the right-hand motor rule, the palm shows the direction of…
3. Conventional current flows up the page and the field points to the right. What is the force?
4. What is the main job of the split-ring commutator in a DC motor?
5. When is the force on a current-carrying wire in a magnetic field zero?
6. Which device works mainly by the motor principle?
Big idea: The motor principle (F3.4) explains every electric motor. This lesson connects it to interacting magnetic fields (F3.5), introduces the third right-hand rule (F3.2) and its left-hand version (F3.3), and explains the parts of a DC motor (F3.6).
How to help: Ask your teen to show you RHR #3 with their hand and to explain why a motor needs a commutator. A quick look at the motor in an old broken toy (battery removed, adult help with any screws) can show the magnets, coil, commutator and brushes for real.
Common difficulties:
- Mixing up which finger is which in RHR #3. A good memory aid: "thumb for current, fingers for field, palm pushes."
- Using the field of the wire itself instead of the external field when applying the rule.
- Thinking the commutator changes the battery's current into AC. It only reverses the current inside the coil.
- Forgetting that reversing both current and field leaves the force unchanged.