What is the inductance L of a 0.40 m long air-filled coil 3.2 cm in diameter containing 10,000 loops?
To calculate the inductance (L) of an air-filled coil, we can use the formula for the inductance of a solenoid:
L = (μ₀ * N² * A) / l
where:
μ₀ is the permeability of free space (4π x 10^-7 T m/A)
N is the number of turns or loops
A is the cross-sectional area of the coil
l is the length of the coil
First, let's calculate the cross-sectional area (A) of the coil. The coil is given to have a diameter of 3.2 cm, so the radius (r) is half of that:
r = (3.2 cm) / 2 = 1.6 cm = 0.016 m
The cross-sectional area (A) of the coil is then:
A = π * r^2 = π * (0.016 m)^2 = 0.00080424 m²
Next, we need to calculate the number of turns (N) in the coil, which is given as 10,000.
Now, we have all the values needed to calculate the inductance (L):
L = (μ₀ * N² * A) / l
= (4π x 10^-7 T m/A) * (10,000²) * (0.00080424 m²) / 0.40 m
Simplifying this equation will give us the final result for the inductance (L).