Answer:
a) 43.2 Jm⁻³
b) 0.0941 J
Explanation:
A = area of cross-section = 23 cm² = 23 x 10⁻⁴ m²
l = length of solenoid = 94.9 cm = 0.949 m
L = inductance of solenoid
N = Number of turns = 809
i = current = 9.70 A
Inductance is given as
L = μ₀ N² A l⁻¹
L = (12.56 x 10⁻⁷) (809)² (23 x 10⁻⁴) (0.949)⁻¹
L = 0.002
V = Volume = Al = (23 x 10⁻⁴) (0.949) = 21.8 x 10⁻⁴ m³
Energy density is given as
U = (0.5) L i² V⁻¹
U = (0.5) (0.002) (9.70)² (21.8 x 10⁻⁴)⁻¹
U = 43.2 Jm⁻³
b)
Total energy is given as
E = (0.5) L i²
E = (0.5) (0.002) (9.70)²
E = 0.0941 J
