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### Course: Physics library > Unit 18

Lesson 3: Measuring magnetic fields# Inverse cube law (deflection method)

Attempt to measure the change in force of a magnet over a distance using the deflection of a compass. What is wrong with this approach? Created by Brit Cruise.

## Want to join the conversation?

- I think it's because the relationship isn't linear. Gravitational force is m1m2/r^2, electrostatic force is q1q2/r^2, electricity and magnetism have been unified. Is there a pattern here? Is magnetic force something/distance^2?(10 votes)
- I have always thought of this in terms of the surface area of a sphere, which is expressed by Area= 4*pi*radius^2. As you can see, the variable which changes is the radius, which is squared. The same force is being spread out over a larger surface area as the distance increases, thus you are looking for a reciprocal quantity, hence 1/radius^2.

Less photons, smaller wave height, lower probability density, whatever it is, it's always struck me as an elegant way to think about it as a spherical surface expanding out from a point source. A kind of cute isomorphism.

I have no idea if this is a valid way of thinking about these things, however. Maybe someone can tell me why I'm an idiot for thinking this way.(17 votes)

- The compass needle is not a fixed, dimensionless point; the needle has length. The three far locations seem to check out, but the final two don't fit that model. Perhaps the difficulty is that the needle is getting closer to the magnet? The magnet is not directed at the very center of the needle? The needle itself provides shielding? The needle is trying to align with the combined field of both the Earth and local magnet?(5 votes)
- No, the problem with the experiment was that the ruler wasn't offset so the magnet could be at the 90 degree mark. Move the ruler over so the magnet could be directly center of that point and the numbers would work out.(3 votes)

- To account for the fact that the center of the compass seems 3 cm from the zero of the meter stick, we should add 3cm to all distances?(5 votes)
- We use sine to describe the angle relationship? Why?(3 votes)
- Soh Cah Toa <-----Learn what this is

(Sine, Cosine, Tangent), is an easy way to geometrically represent it. Much easier than going into trigonometry, and much better explained/represented than just stating the angle facts.(1 vote)

- Is this question similar to that of inverse square law ( method of oscillation) ? Only different cause in this video & question the compass is deflecting the magnetic energy in the magnet no matter how close the magnet is getting ?(3 votes)
- I dont even get what this is doing.. I dont get what the inverse square law even is.. I have an exam in two days and i was told to know what this is and how to do problems with it, which i dont. So if anyone could explain the just of it, that would be VERRRYYYY helpful! I also am in 8th grade adv. physics, so dont get to confusing please. I read somethig in my txtbook about the closest is one square, then 1/4th, then 1/9th but i dont get how they got that. Is it like squaring the number? I.E. 3squared is 9 etc. Thanksssss!!(1 vote)
- The numbers come from the fact that approximately, if you double the distance, you quarter the force. If you triple the distance, the force will be divided by 9. Generally, multiply the distance by n, the distance drops by a factor of n^2. In other words, you multiply the distance by 1/n^2. Now it should be clear why the law is called the inverse (reciprocal) square.(4 votes)

- If the distance of the deflection angle went past the max, what would you think would happen, even if it was possible?(1 vote)
- The deflection in percentage is inversely correlated with the strength of the magnet. Let x equal to the strength of the magnet as represented by a multiple of the strength of Earth's magnetic field. Let d equal to the deflection expressed as a proportion (where 0 means none and 1 means max)

d = x/(x + 1)

Solve for x in terms of d and y

d*x + d = x

x = d*x + d

x - d*x = d

x(1 - d) = d

x = d/(1 - d)

If the inverse cube law holds true, the deflection x, m cm away from the compass should be about:

x = 0.2 * (25/m)^3

And Adjusting for the Values in the Video

When m = 25, d = 0.17 and x = 0.20.

When m = 20, d = 0.25 and x = 0.33.

Expected Value: 0.39

When m = 15, d = 0.45 and x = 0.81.

Expected Value: 0.93

When m = 10, d = 0.70 and x = 2.33.

Expected Value: 3.13(1 vote) - Do the resulting curve (function) is an constant radius arc ?!(1 vote)
- would the answer differ if you had a stronger/weaker magnet?(1 vote)
- Yes because different magnets have different magnetic pulls. Most likely, the denser ones will have more pull.(1 vote)

## Video transcript

(Vertical axis) deflection angle. (Vertical axis) deflection angle,
(Horizontal axis) distance. (Vertical axis) deflection angle,