Magnetism and magnetic fields Revision Notes

The Ideal Transformer Model (Higher)

An ideal transformer operates with 100% efficiency, meaning all the electrical power supplied to the primary coil is transferred to the secondary coil without any energy loss. This implies that the power in the primary circuit (P_primary) is equal to the power in the secondary circuit (P_secondary). Since Power (P) = Potential Difference (V) × Current (I), for an ideal transformer, we can write Vp × Ip = Vs × Is. This idealisation simplifies the analysis of transformer behaviour and allows us to derive the fundamental relationships between voltage, current, and turns ratio. In reality, transformers always have some energy losses due to resistance in the coils, eddy currents in the core, and hysteresis losses, but the ideal model provides a close approximation for many applications.

Relationship between Voltage and Turns (Higher)

The core principle governing transformers is electromagnetic induction. An ideal transformer's operation depends on the direct proportionality between the induced potential difference across a coil and the number of turns in that coil, given a constant rate of change of magnetic flux. Specifically, the ratio of the potential difference across the primary coil (Vp) to the potential difference across the secondary coil (Vs) is equal to the ratio of the number of turns in the primary coil (Np) to the number of turns in the secondary coil (Ns). This can be expressed mathematically as: Vp / Vs = Np / Ns. This equation is crucial for calculating unknown voltages or turns given the other parameters and for understanding whether a transformer is stepping up or stepping down the voltage. This relationship holds true because the changing magnetic flux linked with each turn in the primary coil also links with each turn in the secondary coil (assuming an efficient core). Thus, the induced EMF per turn is effectively the same in both coils.

Step-Up vs. Step-Down Transformers (Higher)

Transformers are categorised as either 'step-up' or 'step-down' based on how they alter the potential difference. A step-up transformer increases the potential difference from the primary to the secondary coil. This occurs when the number of turns in the secondary coil (Ns) is greater than the number of turns in the primary coil (Np). Consequently, because Vp / Vs = Np / Ns, if Ns > Np, then Vs > Vp. Conversely, a step-down transformer decreases the potential difference from the primary to the secondary coil. This happens when the number of turns in the secondary coil (Ns) is less than the number of turns in the primary coil (Np). In this case, if Ns < Np, then Vs < Vp. Step-up transformers are common in power stations to increase voltage for efficient long-distance transmission, while step-down transformers are used near homes and businesses to reduce voltage to safe and usable levels.

H: Principle of Operation and Components

A transformer operates on the principle of electromagnetic induction. It comprises a primary coil and a secondary coil, both wound around a laminated soft iron core. The primary coil is connected to an alternating current (AC) supply, which generates a continually changing magnetic field. This field is efficiently channelled through the soft iron core, which is chosen for its ability to be easily magnetised and demagnetised, enhancing the magnetic flux linkage between the coils.

H: Mutual Induction and AC Requirement

The changing magnetic field from the primary coil passes through the secondary coil, inducing an alternating electromotive force (e.m.f.) and thus an alternating current in the secondary circuit (if closed). This process is known as mutual induction. It is crucial that the input current is alternating because a steady direct current (DC) produces a constant magnetic field, which would not induce an e.m.f. in the secondary coil, as induction requires a changing magnetic flux.

H: Voltage Transformation and Turns Ratio

The voltage induced in the secondary coil is directly proportional to the ratio of the number of turns in the secondary coil (N_s) to the number of turns in the primary coil (N_p). The relationship is given by the ideal transformer equation: V_s / V_p = N_s / N_p. A transformer with more turns in the secondary coil than the primary coil is a 'step-up' transformer, increasing voltage. Conversely, a 'step-down' transformer has fewer turns in the secondary coil, decreasing voltage.

H: Iron Core Lamination and Energy Losses

The soft iron core is laminated, meaning it is made of thin sheets insulated from each other. This lamination significantly reduces energy losses caused by eddy currents. Eddy currents are unwanted circulating currents induced within the bulk of the conductive core itself by the changing magnetic field. These currents generate heat, leading to energy dissipation. By laminating the core, the pathways for eddy currents are broken up, increasing resistance and therefore reducing their magnitude and associated power loss.

Microphone Action (Higher)

A microphone converts sound energy into electrical energy. Sound waves are pressure variations in the air that cause a diaphragm to vibrate. This diaphragm is connected to a coil of wire. The coil is situated within a magnetic field produced by a permanent magnet. As the diaphragm vibrates, the coil moves back and forth within the magnetic field. This movement causes the coil to cut magnetic field lines, inducing a voltage across the coil. This induced voltage drives a varying current in the electrical circuit, which corresponds to the original sound wave's pattern of pressure variations. The amplitude of sound waves affects the magnitude of induced current, and the frequency of sound waves affects the frequency of the induced current.

Loudspeaker and Headphone Action (Higher)

Loudspeakers and headphones convert electrical energy back into sound energy. An electrical current, representing the sound, is fed into a coil of wire (the voice coil). This voice coil is attached to a cone (in a loudspeaker) or a diaphragm (in headphones). The voice coil is placed within the magnetic field of a strong permanent magnet. According to the motor effect, when current flows through a conductor in a magnetic field, a force is exerted on the conductor. As the electrical current varies, the force on the voice coil also varies, causing it and the attached cone/diaphragm to vibrate. These vibrations create pressure variations in the surrounding air, which are perceived as sound waves. The frequency and amplitude of the varying electrical current determine the pitch and loudness of the reproduced sound, respectively.

Electromagnetic Induction in Microphones (Higher)

The operation of a microphone is an example of electromagnetic induction. When a conductor (the coil) moves through a magnetic field, or when the magnetic field through a conductor changes, an electromotive force (e.m.f.) is induced across the conductor, causing a current to flow if the circuit is complete. In a microphone, the mechanical energy from the sound waves is converted into electrical energy via this principle. The diaphragm's vibrations cause the coil to move, effectively 'cutting' the magnetic flux lines, which induces the varying electrical signal.

Motor Effect in Loudspeakers/Headphones (Higher)

The functioning of loudspeakers and headphones is an application of the motor effect. When an electric current flows through a conductor placed in a magnetic field, the conductor experiences a force. The direction of this force is given by Fleming's left-hand rule. In these devices, the varying electrical current supplied to the voice coil interacts with the magnetic field of the permanent magnet, producing a changing force. This force causes the voice coil and attached diaphragm/cone to move, generating the sound waves. The motor effect is essentially the conversion of electrical energy into mechanical energy.

The Motor Effect - Foundation for Rotation (Higher)

The motor effect is fundamental to how electric motors operate. It states that a current-carrying conductor placed in a magnetic field experiences a force. The direction of this force is perpendicular to both the direction of the current and the direction of the magnetic field. Fleming's Left-Hand Rule is a mnemonic used to determine the direction of this force: the thumb represents the direction of the Force, the forefinger represents the direction of the magnetic Field (North to South), and the middle finger represents the direction of the Current (+ to -). In an electric motor, the magnetic field is typically provided by permanent magnets or electromagnets, and the current flows through a coil of wire. This interaction between the current and the magnetic field generates the mechanical force required for rotation.

Components of a Simple DC Electric Motor (Higher)

A simple DC electric motor primarily consists of several key components working in conjunction to produce continuous rotation. The armature is a coil of wire, often wound around a soft iron core, which rotates within the magnetic field. Permanent magnets create a stationary magnetic field that interacts with the current in the armature. The commutator is a crucial split-ring device that reverses the direction of the current in the armature coil every half turn, thereby maintaining the direction of the turning force and ensuring continuous rotation in one direction. Carbon brushes are used to make electrical contact with the spinning commutator, providing a path for the external DC power supply to reach the armature. The combination of these parts allows for the efficient conversion of electrical energy into kinetic energy.

How Motor Rotation is Achieved (Higher)

When current flows through the armature coil, each side of the coil within the magnetic field experiences a force. Due to the opposite direction of current flow in the parallel sides of the coil (one side going 'in', the other 'out' relative to the magnetic field), the forces on these sides will be in opposite directions. These two opposing forces act on different points of the coil, creating a turning effect or torque. For example, if one side is pushed up and the other down, the coil will rotate. After half a rotation, the sides of the coil have swapped their positions within the magnetic field. Without a commutator, the forces would reverse, causing the coil to oscillate or stop. The commutator ensures that the current direction in each side of the coil reverses relative to the magnetic field, so the forces always act in the same rotational direction, leading to continuous, unidirectional rotation.

Factors Affecting Motor Strength and Speed (Higher)

The strength and speed of an electric motor's rotation can be controlled by altering several factors. Increasing the current flowing through the coil directly increases the magnitude of the force experienced by the conductor, leading to a stronger turning effect and faster rotation. Using a stronger magnetic field (either by using more powerful permanent magnets or increasing the current in electromagnets) will also increase the force on the coil, resulting in a more powerful and faster motor. Additionally, increasing the number of turns in the coil or increasing the area of the coil within the magnetic field will enhance the overall motor effect, as more current-carrying segments are interacting with the magnetic field, thereby increasing the total turning force and the speed of rotation.