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A solenoid is formed by winding 25.3 m of insulated silver wire around a hollow cylinder. The turns are wound as closely as possible without overlapping, and the insulating coat on the wire is negligibly thin. When the solenoid is connected to an ideal (no internal resistance) 3.21-V battery, the magnitude of the magnetic field inside the solenoid is found to be 6.79 10-3 T. Determine the radius of the wire. (Hint: Because the solenoid is closely coiled, the number of turns per unit length depends on the radius of the wire.)

PLEASE HELP:)

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5 answers
  1. calculete turns/length as in the hint. Then use your formula.

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    👤
    bobpursley
  2. to calculate turns/length, would it be N/R = 2B/mu*I? but then what is my I value? or am I going about this the completely wrong way?

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  3. I figured out the right equation. It is B=mu*n*I but I still don't know how to figure out what I is

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  4. L is the length of the solenoid
    N is the number of turns
    d is the diameter of the wire
    r is the radius of the solenoid (of the turn)
    Resistance R=ρx/A=4ρx/πd²
    ρ=1.6•10⁻⁸ Ω•m
    μ₀=4π•10⁻⁷ H/m
    U = 3.21 V
    B=6.79•10⁻³ T
    x=25.3 m
    r₀=?
    L=Nd => N=L/d
    B= μ₀nI= μ₀•(N/L)•(U/R)=
    = μ₀•(N/Nd)•(U πd²/4ρx )=
    = μ₀•πUd/4ρx.
    The radius of the wire is
    r₀=d/2=4ρxB/2μ₀•πU=
    =2ρxB/μ₀•πU =…

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  5. thank you so much!!!

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