Answer:
P = 0.3668 W = 366.8 mW
Explanation:
First we calculate the total no. of coils of solenoid:
N = L/d
where,
N = Total No. of Coils = ?
L = Length of Tube = 85.5 cm = 0.855 m
d = diameter of wire = 0.12 cm = 0.0012 m
Therefore,
N = 85.5 cm/0.12 cm
N = 712.5 = 712 turns
Now, we use formula for magnetic field strength of solenoid:
B = μ₀NI/L
where,
B = Magnetic Field = 9.6 mT = 0.0096 T
μ₀ = 4π x 10⁻⁷ N/A²
I = Current = ?
Therefore,
0.0096 T = (712)(4π x 10⁻⁷ N/A²)(I)/(0.855 m)
I = 0.0096/0.00104
I = 9.17 A
Now we will find resistance of wire:
R = ρLw/A
where,
R = Resistance of copper wire = ?
ρ = resistivity of copper = 1.7 x 10⁻⁸ Ωm
Lw = Length of wire used = 2πrN = πdN = π(0.0012 m)(712) = 2.68 m
A=cross-sectional area of wire = πr² = πd²/4 = π(0.0012 m)²/4 = 1.13 x 10⁻⁶ m²
Therefore,
R = (1.7 x 10⁻⁸ Ωm)(2.68 m)/(1.13 x 10⁻⁶ m²)
R = 0.04 Ω
No, the delivered can be calculated as:
P = VI = (IR)I = I²R
P = (9.17 A)²(0.04 Ω)
P = 0.3668 W = 366.8 mW
