A thin 12 cm long solenoid has a total of 460 turns of wire and carries a current of 2.1 A. Calculate the magnitude of the field inside near the center.
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Well, if I were a magnetic field, I'd probably hide in the center of a solenoid too. It's like a cozy little cave in there! But enough about my magnetic field fantasies, let's do some calculations!
To find the magnitude of the magnetic field inside a solenoid, you can use the formula:
B = μ₀ * (N/L) * I
Where B is the magnetic field, μ₀ is the permeability of free space (which is approximately 4π * 10⁻⁷ T m/A), N is the number of turns of wire, L is the length of the solenoid, and I is the current.
Let's plug in the values:
B = (4π * 10⁻⁷ T m/A) * (460 turns / 0.12 m) * 2.1 A
B = 9.85 × 10⁻⁴ T
So, the magnitude of the magnetic field near the center of the solenoid is approximately 9.85 × 10⁻⁴ Tesla. But don't worry, it won't make your hair stand on end unless you've been wearing a clown wig all day!
To calculate the magnitude of the magnetic field inside a solenoid near its center, you can use the equation:
B = μ₀ * n * I
Where:
B is the magnetic field strength
μ₀ (mu-zero) is the permeability of vacuum, which is a constant with a value of 4π × 10⁻⁷ T · m/A
n is the number of turns per unit length of the solenoid, calculated as n = N / L, where N is the total number of turns in the solenoid and L is the length of the solenoid
I is the current flowing through the solenoid
Given:
Total length of the solenoid (L) = 12 cm = 0.12 m
Total number of turns (N) = 460
Current flowing through the solenoid (I) = 2.1 A
First, calculate the number of turns per unit length (n):
n = N / L = 460 / 0.12 = 3,833.33 turns/m
Now, substitute the values into the equation:
B = (4π × 10⁻⁷ T · m/A) * (3,833.33 turns/m) * (2.1 A)
Calculating this expression will give you the magnitude of the magnetic field inside the solenoid near its center.