Math in the Workplace - Algebra/Analysis and Probability

HEWLETT-PACKARD Computing and Imaging Products and Services Magnetic Recording Engineer	Job Description: Design digital magnetic recording systems for use in hard disk drives.

Problem:

A magnetic recording engineer wants to determine the minimum write current (I_w) he can use to drive a head to write magnetic transitions (bits of information) onto a disk in a disk drive.

The head cannot get any closer than 25 nanometers (1 nanometer = 1 x 10^-9 meters) to the surface of the disk. The magnetic field at the head gap (H_g) is roughly equal to product of the number of windings on the head (N) times the write current (expressed in amps), divided by the distance of the gap (G).

The magnetic field is expressed in a couple of terms, Oersteds (Oe) and Amp•Turns/Meters. One Orested is equal to 80•pAmp•Turns/Meter.

The head has 48 turns (or windings) and the gap distance is 1 micrometer (1 x 10^-6 meters or 1 µm). From previous modeling, he knows that the magnetic field decreases with distance away from the gap, such that it is roughly one half of H_g when the head is 25 nanometers away from the disk. He knows there is a demagnetizing field (H_d) that occurs inside the disk during the write process.

This field opposes the field from the head. Previous calculations showed that H_d is 500 Oersteds. The net field for writing (H_x) must be greater than the coercivity (H_c) of the media plus the demagnetizing field. The coercivity of the media has been measured at 2000 Oersteds.

HEWLETT-PACKARD

Solution:

H_x > H_c + H_d

H_c + H_d = 2000 Oe + 500 Oe

= 2500 Oe

H_x = 0.5 H_g

Therefore, H_g = 2 • H_x > 5000 Oe

1 Oe = 80 • p Amp • Turns / Meter, abbreviated (A • T) / m

Therefore, H_g > 5000 Oe (80 • p) (A • T)/m

H_g > 1.26 • 10⁶ A • T/m

H_g = (I_w • N)/G

I_w = H_g • G/N = (1.26 • 10⁶ A • T/m)(1 • 10^-6 m) / 48 T

I_w > 0.026 Amps or 26 • 10^-3 Amps (26 milliamps)

Math in the Workplace: Overview