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?

Answer 1

Step-by-step 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