Homework on Magnetic Storage (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material and be in your own words.Students who turn in identical (or close to identical) homework assignments will be asked to explain their answers orally to the TA or prof. A student who cannot explain how he or she arrived at a given answer will be charged with academic dishonesty.

You should show all of your calculations (neatly) and justify all of your answers for full credit.

1. A sequence of domains on a magnetic tape is NS SN SN NS SN NS NS SN NS. What bits do this represent? What is the decimal equivalent of the binary number represented?
The magnetic field must change directions between bits, so the end of the 2nd domain cannot be the end of a bit. Thus the data must start with the 2nd domain. We then have SN SN = 0, NS SN = 1, NS NS = 0, and SN NS = 1. Thus the data is 0101 binary = 5 decimal.

2.
A loop of wire is in a magnetic field as shown to the right. Under which of the following conditions will current be induced in the loop? (a) The loop is sitting in the field. (b) The loop moves to the right in the field. (c) The loop moves upwards out of the field.
Only in (c) is there any change to the field passing through the loop, so that is the only case where there will be an induced current.

3. A loop of wire of radius 4.3 cm (0.043 m) is in a changing magnetic field. The field decreases by 0.062 tesla every second. What is the emf induced in the loop?
Since the area is constant, the induced emf is equal to the area multiplied by the rate of change of the field. 3.14159 * (0.043 m)² * 0.062 T/s = 3.6 x 10^-4 V (Note: The units do in fact work out, since a tesla is equal to a volt-second per square meter.)

4. An electron (e = 1.6 x 10-19 C) moves with a speed of 220 m/s through a magnetic field of strength 0.56 Tesla, at a right angle to the field lines. What is the magnetic force on the electron?
|F| = |q v B|, because of the right angle (sin q = 1); (1.6 x 10^-19 C) (220 m/s) (0.56 T) = 1.28 x 10^-17 N

5. Describe the physical principles behind magnetoresistance and giant magnetoresistance. How are they alike? How are they different? Which is the bigger effect? Which uses the simpler technology?
Magnetoresistance makes use of the fact that current is simply moving charges, and a magnetic field can exert a force on these charges. Specifically, the field forces the charges into a narrower section of the wire, thus increasing resistance; stronger fields create more resistance. The field can be measured by monitoring the change in current.
Giant magnetoresistance is similar only in that a magnetic field creates a change in resistance. It operates by taking advantage of the inherent magnetic field of electrons. Electrons passing through a field tend to be scattered much less if their fields line up with the external field, creating a lower resistance. This effect is much larger than magnetoresistance, allowing for much more sensitive devices. However, the equipment is much more complicated; all that is needed for magnetoresistance is a loop of wire.
Both effects are substatially larger than induction. Magnetoresistance utilizes a particular simple measurement technique- measuring the resistance through a wire. Super magnetoresistance use the same measurement technique but requires a superlattice which is relatively difficult to construct. However, the relative effect of super magnetoresistance is far greater than magnetoresistance.

1.	A sequence of domains on a magnetic tape is NS SN SN NS SN NS NS SN NS. What bits do this represent? What is the decimal equivalent of the binary number represented? The magnetic field must change directions between bits, so the end of the 2nd domain cannot be the end of a bit. Thus the data must start with the 2nd domain. We then have SN SN = 0, NS SN = 1, NS NS = 0, and SN NS = 1. Thus the data is 0101 binary = 5 decimal.
2.	A loop of wire is in a magnetic field as shown to the right. Under which of the following conditions will current be induced in the loop? (a) The loop is sitting in the field. (b) The loop moves to the right in the field. (c) The loop moves upwards out of the field. Only in (c) is there any change to the field passing through the loop, so that is the only case where there will be an induced current.
3.	A loop of wire of radius 4.3 cm (0.043 m) is in a changing magnetic field. The field decreases by 0.062 tesla every second. What is the emf induced in the loop? Since the area is constant, the induced emf is equal to the area multiplied by the rate of change of the field. 3.14159 * (0.043 m)² * 0.062 T/s = 3.6 x 10^-4 V (Note: The units do in fact work out, since a tesla is equal to a volt-second per square meter.)
4.	An electron (e = 1.6 x 10-19 C) moves with a speed of 220 m/s through a magnetic field of strength 0.56 Tesla, at a right angle to the field lines. What is the magnetic force on the electron? \|F\| = \|q v B\|, because of the right angle (sin q = 1); (1.6 x 10^-19 C) (220 m/s) (0.56 T) = 1.28 x 10^-17 N
5.	Describe the physical principles behind magnetoresistance and giant magnetoresistance. How are they alike? How are they different? Which is the bigger effect? Which uses the simpler technology? Magnetoresistance makes use of the fact that current is simply moving charges, and a magnetic field can exert a force on these charges. Specifically, the field forces the charges into a narrower section of the wire, thus increasing resistance; stronger fields create more resistance. The field can be measured by monitoring the change in current. Giant magnetoresistance is similar only in that a magnetic field creates a change in resistance. It operates by taking advantage of the inherent magnetic field of electrons. Electrons passing through a field tend to be scattered much less if their fields line up with the external field, creating a lower resistance. This effect is much larger than magnetoresistance, allowing for much more sensitive devices. However, the equipment is much more complicated; all that is needed for magnetoresistance is a loop of wire. Both effects are substatially larger than induction. Magnetoresistance utilizes a particular simple measurement technique- measuring the resistance through a wire. Super magnetoresistance use the same measurement technique but requires a superlattice which is relatively difficult to construct. However, the relative effect of super magnetoresistance is far greater than magnetoresistance.