Electromagnetic (EM) Induction

Electromagnetic Induction

Electromagnetic induction occurs when a changing magnetic field induces a potential difference (voltage) across a conductor. This happens when there is relative motion between a magnet and a coil of wire.

If a magnet is moved into or out of a coil, or if the coil moves in a magnetic field, the magnetic flux through the coil changes. This change in magnetic flux induces a potential difference in the coil, causing an electric current if the circuit is complete.

Magnetic flux is the measure of the magnetic field passing through a given area (such as a coil). A change in magnetic flux is essential for induction.

The direction of the induced current is given by Lenz's Law, which states: the induced current flows in such a direction that its magnetic field opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy.

This effect is the basis of the generator effect, where mechanical energy is converted into electrical energy by rotating a coil in a magnetic field, continuously changing the magnetic flux and inducing an alternating potential difference.

For example, when a magnet is pushed into a coil, the induced current flows in one direction. When the magnet is pulled out, the current reverses direction.

The induced potential difference depends on:

• The speed of movement of the magnet or coil (faster changes induce a larger voltage)
• The strength of the magnetic field
• The number of turns in the coil
• The area of the coil

For instance, if a magnet is moved quickly into a coil, the induced voltage is greater than if it is moved slowly.

The potential difference induced in the coil is alternating if the magnet or coil moves back and forth, producing an alternating current (AC).

Example: If a magnet is pushed into a coil and the induced current is measured as 0.5 A in one direction, pulling the magnet out at the same speed will induce a current of 0.5 A in the opposite direction.

Transformers

Transformers use electromagnetic induction to change the size of an alternating potential difference (voltage). They consist of two coils of wire, the primary coil and the secondary coil, wound around an iron core.

When an alternating current flows in the primary coil, it creates a changing magnetic field in the iron core. This changing magnetic field induces an alternating potential difference in the secondary coil.

Depending on the number of turns in each coil, the transformer can either increase or decrease the voltage:

• Step-up transformer: The secondary coil has more turns than the primary coil, so the voltage increases.
• Step-down transformer: The secondary coil has fewer turns than the primary coil, so the voltage decreases.

The relationship between the voltages and the number of turns is given by the transformer equation:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

• $V_p$ = potential difference across the primary coil
• $V_s$ = potential difference across the secondary coil
• $N_p$ = number of turns on the primary coil
• $N_s$ = number of turns on the secondary coil

Ignoring energy losses, the power input to the primary coil equals the power output from the secondary coil:

$$V_p I_p = V_s I_s$$

Where $I_p$ and $I_s$ are the currents in the primary and secondary coils respectively.

For example, if a step-up transformer increases voltage from 230 V to 4600 V, and the primary coil has 100 turns, the secondary coil must have:

$$N_s = N_p \times \frac{V_s}{V_p} = 100 \times \frac{4600}{230} = 2000 \text{ turns}$$

AC & High Voltage Transmission

Transformers only work with alternating current (AC) because a changing magnetic field is needed to induce a voltage in the secondary coil. Direct current (DC) produces a constant magnetic field, so no voltage is induced.

The National Grid uses high voltages to transmit electrical power over long distances. This is because:

• Power loss in cables is proportional to the square of the current ($P = I^2 R$)
• To reduce power loss, current must be kept low
• Using a high voltage allows the same power to be transmitted with a lower current

The National Grid steps up the voltage to hundreds of thousands of volts using step-up transformers near power stations. This reduces current and minimises energy loss during transmission.

Near homes and businesses, step-down transformers reduce the voltage to safer, usable levels (e.g., 230 V in the UK).

In summary, transformers play a vital role in the National Grid by enabling efficient transmission of electricity at high voltages and safe distribution at low voltages.

Applications of EM Induction

The generator effect is used in many practical devices:

• Electric generators: Convert mechanical energy into electrical energy by rotating coils in magnetic fields, producing an alternating potential difference.
• Microphones: Sound waves cause a coil attached to a diaphragm to move in a magnetic field, inducing a varying potential difference that corresponds to the sound.

The potential difference induced in a coil during rotation varies with time and can be graphed as a sine wave, showing alternating positive and negative values as the coil rotates through different angles in the magnetic field.

The graph of potential difference against time for a rotating coil in a magnetic field is sinusoidal because the rate of change of magnetic flux changes continuously as the coil rotates.

For example, when the coil is perpendicular to the magnetic field, the magnetic flux is maximum but not changing, so the induced voltage is zero. When the coil is parallel to the magnetic field, the flux is zero but changing fastest, so the induced voltage is at its peak.

Example: A coil rotates in a magnetic field producing an alternating voltage that varies between +12 V and -12 V every 0.02 seconds. The frequency of the AC is the reciprocal of the period, so:

$$f = \frac{1}{0.02} = 50\, \text{Hz}$$