☰ Contents · Physics

Electromagnetic induction

Lessons 7 · 1 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
7

Electromagnetic induction. Induced electromotive force. Faraday's law

Textbook: pp. 26–28
GoalExplain electromagnetic induction, the Faraday–Maxwell law Eᵢ = –N·ΔΦ/Δt and Lenz's rule, and calculate the induced EMF and current.
New words
electromagnetic induction · elektromagnit induksiyainduced current · induksion tokinduced EMF · induksiya EYuKLenz's rule · Lens qoidasi
Explanation

In 1831 Faraday found that a current appears in a closed circuit when the magnetic flux through it changes; this phenomenon is electromagnetic induction and the current is the induced current. The current exists only while the flux is changing: if the magnet rests inside the coil the galvanometer reads zero; it does not matter how the flux is changed (moving the magnet, moving the coil, changing a current, rotating the circuit). The Faraday–Maxwell law: the induced EMF in a circuit equals the rate of change of the magnetic flux, Eᵢ = –ΔΦ/Δt, and for a coil of N turns Eᵢ = –N·ΔΦ/Δt (unit: volt, 1 V = 1 Wb/s). If the circuit has resistance R, the induced current is I = |Eᵢ|/R. The minus sign expresses Lenz's rule: the induced current has such a direction that its own magnetic field opposes the change of the flux that produced it (the field opposes the flux if it grows and supports it if it decreases). In an open (cut) ring an EMF may appear but no current flows, so the ring does not react to the magnet.

Worked examples
In a coil of N = 200 turns the flux grows uniformly from 4 mWb to 10 mWb in 0.3 s. ΔΦ = 6 mWb; |Eᵢ| = N·ΔΦ/Δt = 200·6·10⁻³/0.3 = 4 V.
The flux through a single-turn loop of resistance 2 Ω falls from 0.05 Wb to 0.01 Wb in 0.5 s. |Eᵢ| = 0.04/0.5 = 0.08 V; I = 0.08/2 = 0.04 A = 40 mA. Because the flux decreases, the induced current's field points the same way as the original field.
Class activity

A demonstration shown only by the teacher: in a circuit of a coil and a sensitive galvanometer (or voltmeter) watch the pointer as a magnet is pushed into and pulled out of the coil. Explain how the deflection differs for fast and slow movement and why a resting magnet gives no current. Strong (neodymium) magnets can pinch fingers and damage devices and cards, so handle them carefully.

Practice
1
What is meant by electromagnetic induction?
2
The flux through a coil of 50 turns changes by 0.3 Wb in 0.1 s. What is |Eᵢ| in V?
3
The flux through a circuit of resistance 5 Ω changes uniformly by 1 Wb in 0.2 s. What is the current in A?
4
Why is an aluminium ring pushed away when the north pole of a magnet approaches it?