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

Mariam Lowe

3 November, 11:55

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?

+1

Answers (1)

Know the Answer?

Madelynn Lowe · 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