Faraday, Lenz and mutual induction
Answers are for parents and teachers.
1
The flux through a coil of 250 turns falls from 6.0 × 10⁻³ Wb to 1.0 × 10⁻³ Wb in 0.10 s (positive direction: the direction of the starting flux). Find emf = −N ΔΦ ÷ Δt with its sign.
ΔΦ = 1.0 × 10⁻³ − 6.0 × 10⁻³ = −5.0 × 10⁻³ Wb. emf = −250 × (−5.0 × 10⁻³) ÷ 0.10 = +12.5 V.
2
A coil of 40 turns and area 0.04 m² faces a field that grows from 0.3 T to 0.9 T in 0.2 s (positive direction: the direction of the field). Find the emf with its sign and its size.
ΔΦ = (0.9 − 0.3) × 0.04 = 0.024 Wb. emf = −40 × 0.024 ÷ 0.2 = −4.8 V. The size is 4.8 V; the minus sign shows that the induced current opposes the growth of the flux.
3
An N pole is moved away from the left face of a coil. Which pole does the left face become, and is the induced current clockwise or anticlockwise as seen from the left?
The face must attract the leaving N pole, so it becomes an S pole. A clockwise current makes a face an S pole, so the current is clockwise as seen from the left.
4
A straight wire moves up through a field that points east. In which direction does the induced current flow in the wire?
Thumb up, forefinger east: the middle finger points north.
5
The current in a primary coil falls from 3 A to 0 in 0.03 s and induces 45 V in the secondary. Find M. What emf would be induced if the current fell at twice that rate?
M = 45 × 0.03 ÷ 3 = 0.45 H. At twice the rate the emf is twice as large: 90 V.