Answer:
P = 29.3 W
Step-by-step explanation:
The magnetic field in a solenoid is
B = μ₀ n i
i = B /μ₀ n
where n is the density of turns
We can use a direct rule of proportions or rule of three to find the number of turns, 1 a turn has a diameter of 0.100 cm = 10⁻³ m, in the length of
L= 85.1 cm = 0.851 m how many turns there are
#_threads = 0.851 / 10⁻³
#_threads = 8.50 10³ turns
the density of turns is
n = # _threads / L
n = 8.51 103 / 0.851
n = 104 turn / m
the current that must pass through the solenoid is
i = 8.90 10-3 / 4pi 10-7 104
i = 0.70823 A
now let's find the resistance of the copper wire
R = ρ L / A
the resistivity of copper is ρ = 1.72 10⁻⁸ Ω m
wire area
A = π r²
A = π (5 10⁻⁴)
A = 7,854 10⁻⁷ m²
let's find the length of wire to build the coil, the length of a turn is
Lo = 2π r = ππ d
Lo = π 0.100
Lo = 0.314159 m / turn
With a direct proportion rule we find the length of the wire to construct the 8.5 103 turns
L = Lo #_threads
L = 0.314159 8.50 10³
L = 2.67 10³ m
resistance is
R = 1.72 10⁻⁸ 2.67 10₃ / 7.854 10⁻⁷
R = 5,847 10¹
R = 58.47 ohm
The power to be supplied to the coil is
P = VI = R i²
P = 58.47 0.70823²
P = 29.3 W