Electricity & Magnetism
Magnetism & Electromagnetism
5th Year · 6th Year (Leaving Cert)
- ✓By the end of this lesson students will be able to define magnetic flux density and state its unit.
- ✓By the end of this lesson students will be able to calculate the force on a current-carrying conductor in a magnetic field.
- ✓By the end of this lesson students will be able to explain electromagnetic induction and state Faraday's and Lenz's laws.
- ✓By the end of this lesson students will be able to solve problems involving induced e.m.f. using Faraday's law.
- ✓By the end of this lesson students will be able to apply the transformer equation to ideal transformers (HL).
Key concepts
Magnetic flux density is a measure of the strength of a magnetic field. It is a vector quantity. It is defined as the force per unit current per unit length on a conductor placed perpendicular to the field. The greater the magnetic flux density, the stronger the magnetic field.
Magnetic flux is the total number of magnetic field lines passing normally through a given area. It quantifies the amount of magnetic field passing through a surface.
A current-carrying conductor placed in a magnetic field experiences a force. The magnitude of this force depends on the magnetic flux density (B), the current (I), the length of the conductor within the field (l), and the angle (θ) between the direction of the current and the magnetic field. The direction of the force is given by Fleming's Left-Hand Rule.
Electromagnetic induction is the process of generating an electromotive force (e.m.f.) and, consequently, an electric current in a conductor by changing the magnetic flux through it. This change can be achieved by moving a magnet near a coil, moving a coil in a magnetic field, or changing the current in a nearby coil.
Faraday's Law states that the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux through the circuit. The negative sign in the formula indicates the direction of the induced e.m.f. as described by Lenz's Law.
Lenz's Law states that the direction of the induced current (or e.m.f.) is always such as to oppose the change in magnetic flux that produced it. This law is a direct consequence of the principle of conservation of energy.
A transformer is a device that changes a high alternating voltage to a low alternating voltage, or vice versa, using the principle of mutual induction. For an ideal transformer (one with no energy losses), the ratio of voltages is equal to the ratio of the number of turns in the coils, and inversely proportional to the ratio of currents.
Key facts to remember
- 1Magnetic flux density (B) is measured in Tesla (T).
- 2Magnetic flux (Φ) is measured in Weber (Wb).
- 3Fleming's Left-Hand Rule determines the direction of the force on a current-carrying conductor in a magnetic field.
- 4Electromagnetic induction is the generation of an e.m.f. by a changing magnetic flux.
- 5Faraday's Law quantifies the induced e.m.f.: E = -N (ΔΦ/Δt).
- 6Lenz's Law states that the induced current opposes the change in magnetic flux that produced it, consistent with energy conservation.
- 7Transformers operate on the principle of mutual induction and only work with alternating current (a.c.) (HL).
- 8For an ideal step-up transformer, the secondary voltage is higher than the primary voltage, and the secondary current is lower than the primary current (HL).
Worked examples
Example 1
A straight conductor of length 25 cm carrying a current of 4.0 A is placed in a uniform magnetic field of flux density 0.60 T. Calculate the force on the conductor when it is (a) perpendicular to the field and (b) makes an angle of 30° with the field.
Answer
(a) 0.60 N, (b) 0.30 N
Remember to convert length from cm to m.
Example 2
A coil of 200 turns has a cross-sectional area of 0.03 m². It is placed in a uniform magnetic field of 0.4 T. The coil is rotated from a position where its plane is perpendicular to the field to a position where its plane is parallel to the field in 0.2 s. Calculate the average induced e.m.f.
Answer
12 V
The negative sign in Faraday's Law accounts for Lenz's Law, but when asked for magnitude, the absolute value is usually given.
Example 3
An ideal transformer (HL) has 300 turns in its primary coil and 1500 turns in its secondary coil. If the primary coil is connected to a 230 V a.c. supply, calculate the voltage across the secondary coil. If the current in the primary coil is 0.6 A, calculate the current in the secondary coil.
Answer
Secondary voltage (Vs) = 1150 V, Secondary current (Is) = 0.12 A
This is a step-up transformer, so voltage increases and current decreases in the secondary coil.
Common mistakes
- ✗Confusing magnetic flux (Φ) with magnetic flux density (B) or their units.
- ✗Incorrectly applying Fleming's Left-Hand Rule, leading to errors in force direction.
- ✗Forgetting to convert units (e.g., cm to m, milliseconds to seconds) before performing calculations.
- ✗Not understanding the significance of the negative sign in Faraday's Law (which represents Lenz's Law).
- ✗Assuming transformers can operate with direct current (d.c.) instead of alternating current (a.c.) (HL).
- ✗Mixing up primary and secondary values in the transformer equations, especially for current (HL).
Exam tips
- ★Always draw clear diagrams to visualise the relative directions of magnetic fields, current, and force when using Fleming's Left-Hand Rule.
- ★Ensure all quantities are in SI units (metres, seconds, amperes, teslas, webers) before substituting them into formulae.
- ★When explaining electromagnetic induction, clearly state both Faraday's Law and Lenz's Law, explaining their relationship.
- ★For transformer problems, carefully identify primary and secondary values and use the correct ratios for voltage, turns, and current (HL).
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