The magnitude of the magnetic field in a magnetic resonance imaging (MRI) machine can be as great as B = 2.0T . Under normal circumstances,

Question

The magnitude of the magnetic field in a magnetic resonance imaging (MRI) machine can be as great as B = 2.0T . Under normal circumstances, this field cannot be shut off by just flipping a switch. Instead the magnitude needs to be carefully decreased to zero. In an emergency, however, the magnet can be “quenched” so that B reduces to zero in 20 s. Such a quench can cost thousands of dollars and likely damages the magnets. Assume that the magnetic field exists inside a cylinder of radius R = 400mm and length ? = 500mm .

How much magnetic potential energy is dissipated when the magnetic field is quenched in this way?

What is the average rate at which energy is dissipated?

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Cherry 4 years 2021-08-26T10:55:08+00:00 1 Answers 5 views 0

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  1. diemkieu
    0
    2021-08-26T10:56:49+00:00
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    Answer:

    Explanation:

    Average energy density of a magnetic field

    = (1 / μ₀) x B²

    = ( 1 / 4π x10⁻⁷ )x 2

    = .159 x 10⁷ J / m³

    Volume of space where field exists

    = πr² x L

    3.14 x .4² x .5 m³

    = .2512 m³

    Total energy contained in magnetic field

    = .2512 x .159 x 10⁷

    = 4 x 10⁵ J .

    Rate of dissipation = 4 x 10⁵ / 20 J/s

    = 2 x 10⁴ J /s

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )