What it shows
Far from a magnet the field along its axis falls roughly as the cube of the distance. A compass needle’s deflection, compared with the Earth’s field, lets you check this from a log graph.
The science
In the end-on position, at a distance d much larger than the magnet’s length, the field of a magnet is B ≈ μ0 2M / (4π d³), where M is its magnetic moment. The compass sits in the Earth’s horizontal field B_H, pointing north; the magnet’s field pushes the needle east or west when the magnet’s axis is east to west. The needle settles at an angle θ where tan θ = B / B_H. So tan θ is proportional to 1 / d³ and a straight log-log graph of tan θ against d has a slope close to −3.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A strong bar magnet (neodymium or ferrite bar)
- A small plastic compass
- A long ruler or metre scale
- A wooden table away from iron, phones and steel furniture
- A sheet of paper and a protractor
- Graph paper or log graph paper
Safety
For this project: Neodymium magnets can pinch fingers and break; an adult must handle them and keep them away from phones, cards and pacemakers.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Place the compass on the paper, wait for it to settle pointing north and turn the paper until the needle lies along a north line you draw.
Lay the ruler east to west through the centre of the compass and place the magnet on the ruler with its axis along the line and its north pole facing the compass; measure every distance d from the compass centre to the middle of the magnet.
Slide the magnet to 30 cm from the compass (start further away if θ is already above about 15 degrees) and read the needle’s angle θ from the paper; repeat with the magnet on the other side of the compass and average to cancel stray fields.
Bring the magnet closer in steps (for example 25, 20, 16, 13, 10 and 8 cm), recording θ each time, and stop when θ reaches about 70 degrees, because the needle is too insensitive near 90 degrees.
Calculate tan θ for each distance in a table with columns for d, θ, tan θ.
Plot log (tan θ) against log (d) or use log graph paper and draw the best straight line.
Find the slope of the line and compare it with −3.
What you should see
The log-log graph is close to a straight line with a slope near −3 for the larger distances. At short distances the slope becomes steeper (more negative), because the magnet is no longer very small compared with d.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01How does the field of a small magnet vary on its axis?
Inversely with the cube of the distance, B proportional to 1 / d³.
02What does the compass compare the magnet’s field with?
The horizontal component of the Earth’s field, since tan θ = B / B_H.
03Why average the readings from both sides?
It cancels errors from the compass pivot and the magnet not being exactly in line.
04What does a slope of −3 on a log graph mean?
That tan θ falls as 1 / d³, an inverse cube law.
Take it further
Repeat in the broadside position and show that the field there is half the end-on value at the same distance.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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