Single-phase electricity at 240 V and 50Hz is sometimes transmitted via concentric cables. The conductor of diameter d₁ passes at the center of the cable and acts as the live wire, while the concentric neutral of diameter d₂ surrounds the live conductor. Red PVC separates the two conducting materials, and black PVC is used as the jacket as shown in the simple image below. Calculate the inductance of a 1 m long wire when d₁ = 5.10 mm and d₂ = 10.5 mm.

Two solenoids are placed such that their magnetic fields interact with each other. They have a mutual induction coefficient of M = 4.32 × 10⁻⁴ H. What is the magnitude of the induced emf in solenoid two if the current flowing through solenoid one changes uniformly at a rate of 650 A/s, and is it constant?

An iron rod, characterized by an average permeability μ equal to 1850 times the permeability of free space μ₀, is the core around which two coils are wound. The first coil, with a length of 5 meters, consists of 400 turns, while the second coil has 180 turns. Each turn has a radius of 3 centimeters.

(a) Determine the mutual inductance between these two coils.

(b) If the current in the first coil decreases uniformly from 20 Amperes to zero over a period of 110 milliseconds, what will be the induced electromotive force (emf) in the second coil?