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23 October, 23:49

A researcher would like to perform an experiment in a zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 3.0 m, with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 μT local value of the earth's field. What current is needed in the solenoid's wires?

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  1. 23 October, 23:51
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    I = 2.48 10⁻² A

    Explanation:

    The magnetic field produced by a solenoid disproportionate to the density of turns and the current passing through the wire

    B = μ₀ n I

    Where μ₀ is the magnetic permeability that you are worth 4π 10⁻⁷ N/A²

    Let's calculate the density of turns.

    n = N / L

    n = 5000 / 3.0

    n = 1666.67

    Let's reduce the field to SI units

    B = 52 μT = 52 10⁻⁶ T

    Let's calculate the current

    I = B / μ₀ n

    I = 52 10⁻⁶ / (4π 10⁻⁷ 1666.67)

    I = 2.48 10⁻² A
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