☰ Year plan · Physics

Faraday, Lenz and mutual induction

Week 8 · Chapter 3 Electromagnetic Induction (A): Faraday’s experiment and the induced emf, Faraday’s law emf = −N ΔΦ/Δt, Lenz’s rule, Fleming’s right-hand rule, mutual induction (M, the henry as V·s/A) and the two-coil experiments · 3 lessons
3

Mutual induction between two coils

Physics Sec 3 Term 1, Chapter 3: pp. 60–67
GoalExplain when an emf is induced in a second coil and calculate it from emf = −M ΔI ÷ Δt.
New words
primary and secondary coil · the primary is joined to the cell and switch; the secondary is joined to a galvanometer or a load and has no cellmutual induction · an emf induced in one coil by a changing current in a neighbouring coilhenry (H) · the unit of M: 1 H = 1 V·s/A, an emf of 1 V when the primary current changes at 1 A/s
Explanation

Put two coils close together. The primary is joined to a cell through a switch (and perhaps a rheostat); the secondary is joined to a zero-centre galvanometer and has no cell. The current in the primary makes a field, and part of its flux passes through the secondary. If the primary current is steady, the flux is steady and the secondary shows nothing. The galvanometer deflects only while the primary current changes: when the switch is closed or opened, when the rheostat slider is moved, or when one coil is moved towards or away from the other. The induced emf is emf = −M ΔI ÷ Δt, where ΔI ÷ Δt tells how fast the primary current changes and M is the mutual inductance in henry (H). M is larger with an iron core, with more turns and bigger coils, and when the coils are close together. Lenz’s rule gives the direction: when the primary current rises, the induced current in the secondary flows against the direction of the primary current; when it falls, it flows in the same direction as the primary current.

Action on the primaryPrimary currentSecondary galvanometer
switch closedrises from 0deflects; induced current opposes the primary current
switch kept closedsteadyzero
switch openedfalls to 0deflects the other way; induced current has the same direction as the primary current
Worked examples
M = 0.40 H and the primary current rises from 0 to 3.0 A in 0.020 s. The size of the emf in the secondary is M × ΔI ÷ Δt = 0.40 × 3.0 ÷ 0.020 = 60 V.
An emf of 24 V is induced in the secondary while the primary current falls from 1.5 A to 0 in 0.05 s. M = emf × Δt ÷ |ΔI| = 24 × 0.05 ÷ 1.5 = 0.8 H.
The primary carries a steady 5 A for a long time. ΔI = 0, so the emf in the secondary is 0 V, although the flux through the secondary is large. Only a changing flux induces an emf.
Class activity

Predict and explain, on paper, for a primary and a secondary coil: (1) the switch is closed and left closed for a minute; (2) the switch is opened; (3) the switch is closed and an iron rod is pushed into both coils while the current is steady; (4) the rheostat slider is moved quickly to a higher resistance. Say in each case whether the secondary galvanometer deflects and, if so, whether the induced current has the same direction as the primary current or the opposite.

Practice
1
M = 0.25 H. The primary current falls from 2.0 A to 1.2 A in 0.40 s. Find the size of the secondary emf.
2
M = 1.2 H and the secondary emf is 36 V for 0.01 s. How much does the primary current change in that time?
3
A secondary emf of 15 V is induced while the primary current changes by 2.5 A in 0.05 s. Find M.
4
The switch of the primary is opened. In which direction, compared with the old primary current, does the induced current in the secondary flow?