4.5.3 Magnetic effect of a current (3)
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1.
A solenoid has 100 turns of wire and carries a current of 2A. Describe how the magnitude and direction of the magnetic field inside the solenoid would be affected if the current is increased to 4A. Explain your answer in terms of the relationship between current and magnetic field.
If the current in the solenoid is increased from 2A to 4A, the magnitude of the magnetic field inside the solenoid will increase proportionally. The magnetic field strength is directly proportional to the current. Therefore, doubling the current will double the magnetic field strength. The direction of the magnetic field inside the solenoid will remain the same. The magnetic field lines will still be parallel to the axis of the solenoid, as determined by the right-hand rule (where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field).
2.
Explain how a transformer works, including the relationship between the number of turns in the primary and secondary coils and the voltage output. Give an example of where transformers are used.
A transformer works on the principle of electromagnetic induction. It consists of two coils of wire (the primary and secondary coils) wound around a common iron core. When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field in the iron core. This changing magnetic field then induces an electromotive force (EMF), or voltage, in the secondary coil.
The relationship between the number of turns in the primary (Np) and secondary (Ns) coils and the voltage (V) is given by the following equation: Vs / Vp = Ns / Np.
- If Ns > Np (more turns in the secondary coil), the voltage in the secondary coil (Vs) will be higher than the voltage in the primary coil (Vp). This is a step-up transformer.
- If Ns < Np (fewer turns in the secondary coil), the voltage in the secondary coil (Vs) will be lower than the voltage in the primary coil (Vp). This is a step-down transformer.
- If Ns = Np (equal number of turns), the voltage in the secondary coil (Vs) will be equal to the voltage in the primary coil (Vp). This is an isolation transformer.
Example Application: Transformers are essential components in electrical power transmission and distribution. They are used to step up the voltage for long-distance transmission (reducing current and minimizing energy loss due to resistance) and then step down the voltage for safe use in homes and businesses. Without transformers, transmitting electricity over long distances would be highly inefficient and dangerous. They are found in power stations, substations, and the transformers within appliances like phone chargers and laptop adapters.
3.
A coil of wire with N turns carries a current I. The magnetic field at the centre of the coil is B. Describe how the magnitude and direction of the magnetic field at the centre of the coil would be affected if the number of turns (N) is doubled and if the current (I) is halved. Explain your answers.
Doubling the number of turns (N): The magnitude of the magnetic field produced by a coil is directly proportional to the number of turns. Therefore, if the number of turns is doubled, the magnitude of the magnetic field at the centre of the coil will also double. The magnetic field strength is proportional to the number of turns. The direction of the magnetic field remains the same – it is determined by the right-hand rule (or Fleming's left-hand rule), which dictates the direction of the magnetic field based on the direction of the current and the direction of the curls of the fingers.
Halving the current (I): The magnitude of the magnetic field produced by a coil is also directly proportional to the current. Therefore, if the current is halved, the magnitude of the magnetic field at the centre of the coil will also be halved. The magnetic field strength is proportional to the current. The direction of the magnetic field remains the same – it is determined by the right-hand rule (or Fleming's left-hand rule), which dictates the direction of the magnetic field based on the direction of the current and the direction of the curls of the fingers.