Question

The national high magnetic field laboratory holds the world record for creating the strongest magnetic field. for brief periods of time, their largest multi-shot pulsed magnet can produce magnetic fields in excess of 85 t. to see if such a strong magnetic field could pose health risks for nearby workers, calculate the maximum acceleration the field could produce for na ions (of mass 3.8 × 10-26 kg) in blood traveling through the aorta. the speed of blood is highly variable, but 45 cm/s is reasonable in the aorta

Answer 1

`a = 1.61 * 10^8 m/s^2`

Step-by-step explanation:

Force due to magnetic field on the position of Na+ ions is given as

`F = qvB`

here we know that

`q = 1.6 * 10^(-19) C`

`v = 45 cm/s`

`B = 85 T`

now the force will be given as

`F = (1.6 * 10^(-19))(0.45)(85)`

`F = 6.12 * 10^(-18) N`

now we know that acceleration is given as

`a = (F)/(m)`

`a = (6.12 * 10^(-18))/(3.8 * 10^(-26))`

`a = 1.61 * 10^8 m/s^2`

Answer 2

Newton’s 2nd law states that Force is equal to the product of mass (m) and acceleration (a):

F = m a ---> 1

While in magnetic forces, force can also be expressed as:

F = q v B ---> 2

where,

q = total charge

v = velocity = 45 cm / s = 0.45 m / s

B = the magnetic field = 85 T

First we solve for the total charge, q:

q = 3.8 × 10^-23 g (1 mol / 23 g) (6.022 × 10^23 electrons / mol) (1.602 × 10^-19 C / electron)

q = 1.594 × 10^-19 C

We equate equations 1 and 2 then solve for acceleration a:

m a = q v B

a = q v B / m

a = [1.594 × 10^-19 C * 0.45 m / s * 85 T] / 3.8 × 10-26 kg

a = 160,437,862.2 m/s^2

Therefore the maximum acceleration of Na ions is about 160 × 10^6 m/s^2.