The Motor Effect & Electromagnetic Induction
Tier and scope note. On Combined Science the motor effect, Fleming’s left-hand rule and F = B × I × l are Higher tier only. Electric motors and the split-ring commutator are separate Physics only, so they are not examined on this course.
The Motor Effect
When a conductor carrying an electric current is placed in a magnetic field, it experiences a force. This is called the motor effect. The force arises because the magnetic field around the current-carrying wire interacts with the external magnetic field from the permanent magnet. An equal and opposite force also acts on the magnet itself — this is Newton's third law in action.
The motor effect only occurs when the current and the magnetic field are not parallel. The force is greatest when the current is at right angles (perpendicular) to the magnetic field. If the current is parallel to the field, there is no force.
A current-carrying conductor in a magnetic field experiences a force. The direction of this force can be found using Fleming's left-hand rule.
Fleming's Left-Hand Rule
Fleming's left-hand rule allows you to work out the direction of the force (and therefore the direction the conductor moves) when the current and magnetic field directions are known. Hold your left hand so that the thumb, first finger, and second finger are all at right angles to each other:
- Thumb = direction of the Force (motion)
- First finger = direction of the magnetic Field (north to south)
- Second finger = direction of the Current (conventional, positive to negative)
If either the current or the magnetic field direction is reversed, the force reverses too. If both are reversed, the force stays the same.
Calculating the Force on a Conductor
The size of the force on a current-carrying conductor in a magnetic field can be calculated using the equation:
$$F = B \times I \times l$$
Where \(F\) is the force in newtons (N), \(B\) is the magnetic flux density in tesla (T), \(I\) is the current in amperes (A), and \(l\) is the length of the conductor in the field in metres (m).
A wire of length 0.25 m carries a current of 4 A at right angles to a magnetic field of flux density 0.3 T. Calculate the force on the wire.
\(F = B \times I \times l = 0.3 \times 4 \times 0.25 = 0.3\) N
The force on the wire is 0.3 N.
\(F = B \times I \times l\) — force (N) = magnetic flux density (T) × current (A) × length (m). This equation only applies when the current is at right angles to the magnetic field.
How an Electric Motor Works
An electric motor uses the motor effect to produce rotation. A rectangular coil of wire is placed between the poles of a permanent magnet. When current flows through the coil, one side of the coil is pushed up and the other side is pushed down (by Fleming's left-hand rule), making the coil spin.
A split-ring commutator reverses the direction of the current every half turn, ensuring that the forces on each side of the coil continue to push in the same rotational direction. Without the commutator, the coil would stop and reverse after each half turn.
Electromagnetic Induction
Electromagnetic induction is the process of generating a potential difference (and, if the circuit is complete, a current) by moving a conductor through a magnetic field, or by changing the magnetic field around a conductor. This is the principle behind generators and transformers.
The size and direction of the induced potential difference depend on several factors:
- The speed of movement — faster movement induces a larger potential difference
- The strength of the magnetic field — a stronger field induces a larger potential difference
- The number of turns on the coil — more turns induce a larger potential difference
- The direction of movement or field change — reversing the direction reverses the induced potential difference
The magnetic field produced by the induced current always opposes the original change that caused it. This is known as Lenz's law.
Transformers and the National Grid
A transformer uses electromagnetic induction to change the size of an alternating voltage. It consists of two coils of wire — a primary coil and a secondary coil — wound around a shared iron core. An alternating current in the primary coil creates a changing magnetic field in the iron core, which induces an alternating voltage in the secondary coil.
A step-up transformer has more turns on the secondary coil than the primary, so the output voltage is higher than the input. A step-down transformer has fewer turns on the secondary coil, so the output voltage is lower.
In the national grid, step-up transformers increase the voltage at power stations to reduce the current. Lower current means less energy is wasted as heat in the transmission cables. Step-down transformers then reduce the voltage to safe levels for homes and businesses.
For a 100% efficient transformer, the power input equals the power output. This gives the equation:
$$V_P \times I_P = V_S \times I_S$$
Where \(V_P\) and \(I_P\) are the voltage and current in the primary coil, and \(V_S\) and \(I_S\) are the voltage and current in the secondary coil. If a transformer steps up the voltage, it must step down the current by the same factor (and vice versa), so that power is conserved.
Example: A step-up transformer has a primary voltage of 230 V and a primary current of 10 A. The secondary voltage is 11,500 V. What is the secondary current?
\(V_P \times I_P = V_S \times I_S\)
\(230 \times 10 = 11{,}500 \times I_S\)
\(I_S = \frac{2300}{11500} = 0.2\) A