Consider a long solenoid of radius R and n turns per unit length. The core of the solenoid is comprised of a material with permeability μ. The current in the coils is increasing at a uniform rate dI/dt. (i) Calculate the B-field due to the solenoid and hence the induced E-field using Fara- day's Law. (ii) What is the energy contained in the solenoid per unit length? (iii) What is the amount of energy flowing per unit time (dW/dt) per unit area of the surface of the solenoid (i.e., what is Poynting's vector)? (iv) What is the self-inductance per unit length of the solenoid, L? dW (v) Use your results from part (iii) and (iv) to show that dw = (LI²)

Consider a long solenoid of radius R and n turns per unit length. The core of the solenoid is comprised of a material with permeability μ. The current in the coils is increasing at a uniform rate dI/dt. (i) Calculate the B-field due to the solenoid and hence the induced E-field using Fara- day's Law. (ii) What is the energy contained in the solenoid per unit length? (iii) What is the amount of energy flowing per unit time (dW/dt) per unit area of the surface of the solenoid (i.e., what is Poynting's vector)? (iv) What is the self-inductance per unit length of the solenoid, L? dW (v) Use your results from part (iii) and (iv) to show that dw = (LI²)