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?

Question

Physics

Eric Gentry

16 August, 00:37

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?

+3

Answers (1)

Know the Answer?

Faith Case · Answer 1

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