Electromagnetic Induction

Electromagnetic Induction explains how a changing magnetic field produces an electric current, the discovery by Faraday and Henry that made electric generators, transformers and induction cooktops possible. In this chapter you will study the experiments of Faraday and Henry with magnets and coils, the meaning of magnetic flux, and Faraday's law, which states that the induced emf equals the negative rate of change of magnetic flux. You will use Lenz's law to find the direction of the induced current and see that it follows from conservation of energy. You will derive the motional emf Blv for a rod moving in a magnetic field and analyse the energy and forces involved. The chapter introduces eddy currents and their uses, self-induction and mutual induction, the self-inductance of a long solenoid, the mutual inductance of two coaxial solenoids and the energy stored in an inductor. Finally, you will learn the principle and working of an AC generator and derive the expression e = NBA omega sin(omega t) for its emf.

Detailed Worksheet: Electromagnetic Induction Section A - Definitions (10 marks) 1. Define magnetic flux and write its SI unit. (2 marks) 2. State Faraday's laws of electromagnetic induction. (2 marks) 3. State Lenz's law. Show that it is a consequence of conservation of energy. (2 marks) 4. Define self-inductance and write its SI unit. (2 marks) 5. What are eddy currents? Give two applications. (2 marks) Section B - Calculations and Applications (15 marks) 6. A square loop of side 10 cm is placed in a uniform magnetic field of 0.5 T with its normal making an angle of 60 degrees with the field. Find the magnetic flux through the loop. (3 marks) 7. A square loop of side 10 cm and resistance 0.5 ohm is placed perpendicular to a magnetic field of 0.10 T. The field is reduced steadily to zero in 0.70 s. Find the induced emf and current. (3 marks) 8. A metal rod of length 1.0 m moves at 5 m/s perpendicular to a magnetic field of 0.5 T, sliding on rails connected to a 5 ohm resistor. Find the induced emf, the current, the force needed to keep the rod moving and the power supplied. (3 marks) 9. The current in a coil of self-inductance 0.2 H falls from 10 A to zero in 0.1 s. Find the average induced emf and the energy stored in the coil when the current is 10 A. (3 marks) 10. A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, find the change of flux linkage with the other coil and the induced emf. (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled diagram of an AC generator showing the armature coil, magnetic poles, slip rings and brushes. Draw the graph of emf against time. (4 marks) 12. Draw a diagram showing a bar magnet moving towards a coil, and mark the direction of the induced current using Lenz's law. (3 marks) 13. Draw a diagram of a conducting rod sliding on parallel rails in a magnetic field, showing the induced current, the magnetic force on the rod and the external force. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A coil of 100 turns and area 0.1 m^2 rotates at 50 revolutions per second in a uniform magnetic field of 0.1 T, with its axis perpendicular to the field. Find the maximum emf generated. Explain why the emf is maximum when the plane of the coil is parallel to the field. (5 marks) 15. A magnet is dropped through a long vertical copper tube and falls much more slowly than through a plastic tube. Explain this using Faraday's and Lenz's laws, and discuss the energy conversion. Give one practical use of this effect. (5 marks) 16. A metallic rod of length 1 m rotates with an angular frequency of 400 rad/s about an axis through one end, perpendicular to the rod, in a uniform magnetic field of 0.5 T parallel to the axis. Derive the emf between the ends and calculate it. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Show directions of induced currents and use SI units throughout.