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17 February, 09:33

Two ideal solenoids of radii R and 4 R, respectively, have n turns per meter, and each carries a current of I. Both currents flow in the same direction. The small‑radius solenoid is placed inside the large-radius solenoid so that their axes of symmetry are parallel and separated by a distance d = 2 R. Neglecting any magnetic screening effects, express the magnetic field strength on the axis of the small-radius solenoid analytically in terms of the quantities given and the magnetic permeability of a vacuum, μ 0.

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  1. 17 February, 09:41
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    The formula for the calculation of the magnetic field inside a solenoid is

    B = μo*n*I

    where

    μo: vacuum permeability

    n: turns per meter

    I: current

    The magnetic field inside de solenoid is constant. In the case of a small-radius solenoid inside a large-radius solenoid, the magnetic field inside the small-radius solenoid is the magnetic field generated by itself plus the magnetic field generated by the large-radius solenoid. (The radius of the solenoids does not have to be with the instensity of the magnetic field):

    BT = Bs + Bl

    Bs: magnetic fiel of the small-radius solenoid

    Bl: magnetic fiel of the large-radius solenoid

    Hence:

    BT = 2*μo*n*I
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