How much would 1g of iron weigh at one of the magnetic poles?

Question

Would the magnetic field "going in" at the poles make a difference to the weight of a fixed mass of iron? What about a 1g magnet?

Answer 1

There are two factors at work here, the strength of the magnetic field and the size of the"magnet" that is the Earth.

Magnetic fields are measured in Gauss. The Earth's magnetic field is about 1 Gauss. In contrast, a good strong permanent magnet has a field of around 20,000 Gauss. The stronger the field, the greater the attractive force. The maximum possible stress that can be produced in a 1 Gauss field is 0.004 Pa (0.0000006 psi). I use stress instead of force here because a larger piece is more strongly attracted. For a 1 cm^3 piece of iron, that comes out to a force of 0.00004 gm or 0.4 microNewtons, only about 1/200,000 the force of gravity. The maximum force is proportional to the square of the field strength so a good strong magnet can develop a force of 2,000 times gravity on the same piece of iron.

The second issue is the size of Earth's magnet. This is a much more difficult thing to understand. A magnetic force is not produced by putting a piece of iron in a magnetic field. It is produced when the movement of the iron in the field takes it from a weaker region to a stronger one. A small permanent magnet produces a noticeable force because the magnetic field spreads out rapidly as you move away from the magnet. When you are very close to its poples the change, and thus the force, is rapid. The Earth is a very large magnet and the change in field as you move the iron a short distance is very small, perhaps 1/1,000,000 that of an ordinary magnet.

Puuting all this together, there is a change in forse for a piece of iron at the poles but it is extrememly small, much too small to measure.

Your second question about a 1g magnet changes things a bit, The discussion about the strength of the field still holds but the issue about the change in the field over a distance does not come into play. The attractive force will still be very small. However, there is a tendency of the magnets to rotate so the fields are aligned. This does not require a gradient in the Earth's field. If it were very free to do so, the pole of your magnet would point to the Earth's magnetic pole. This small force is the basis for a magnetic compass.

Answer 2

Good question, shows you're thinking about things critically.

I suspect you want to know if there is significant magnetic force on the 1 gm of iron to make it appear heavier than it would with just the gravitational pull. In fact, it would if the magnetic force were lined up with the pull of gravity.

That assertion comes from w + f = F; where w is the thing we call weight (Mg), f is the magnetic force (kAB^2) due to the magnetic flux from the magnetic pole, and F is the total forces acting on the piece of iron in the direction of the pull of gravity (i.e., towards the center of the Earth). For a given magnetic flux (B), the magnetic force varies as the cross sectional area (A) of the attracted body (e.g., your 1 gm piece of iron). [See source.]

Your 1 gm piece of iron weighs very little (Mg = (1/1000) 9.81) Newtons; so even a little bit of magnetic force will be relatively significant. That is, the magnetic force could very well be a high percentage of all the forces acting on the piece of iron.

But without knowing B and the value for k (which depends in part on the material of the attracted body), the exact force can't be calculated. But we can assert it will be small because of two things.

First, we know the compass needle of a magnetic compass swings around very slowly when aligning with a magnetic pole. That indicates just a low accelerating (moving) magnetic force acting on that needle. Thus, f on that needle is small; so it'll probably be small on a small piece of iron as well.

Second, the A in the magnetic force equation would be very small for a piece of iron of only 1 gm (.001 kg) mass. So the resulting f would probably be likewise small for a given B.

Answer 3

the magnetic attraction between the magnetic pole and the magnet is negligable. The shape of the earth (closer at the poles than the equator to the center of the earth) will have a much greater affect but even that is extremely small.

Answer 4

See the definition in the reference. Weight is the force due to gravity, and is independent of any magnetic field.

Answer 5

I don't think you'd have to go as far as the poles. Weight is effected by gravity so it changes, very slightly, depending on where you are on the planet. It's mass remains the same.

Answer 6

10 ton

Answer 7

1g

Answer 8

no, on those scales it would not affect gravity - which weight is based on

Answer 9

1g.....