Question
A solenoid has a ferromagnetic core, n = 1000 turns per meter, and /= 5.0 A. If B inside the solenoid is 2.0 T, what is x for the core material?
A solenoid has a ferromagnetic core, n = 1000 turns per meter, and /= 5.0 A. If B inside the solenoid is 2.0 T, what is x for the core material?
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Koala Tutor
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To find x, we need to use the formula for the magnetic field inside a solenoid:
B = μ₀ * n * I,
where B is the magnetic field, μ₀ is the permeability of free space (μ₀ = 4π x 10^(-7) T*m/A), n is the number of turns per meter, and I is the current.
Rearranging the equation to solve for x, we get:
x = B / (μ₀ * n * I).
Substituting the given values:
x = 2.0 T / (4π x 10^(-7) T*m/A * 1000 turns/m * 5.0 A).
Simplifying:
x = 2.0 T / (8π x 10^(-3) T*m/A).
Using the value of π (pi) as 3.14:
x = 2.0 T / (8 x 3.14 x 10^(-3) T*m/A).
x ≈ 79.6 m.
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