What it shows
A compass at the centre of a vertical coil set in the magnetic north-south plane is deflected by the coil’s field, and the tangent of the deflection angle is proportional to the current (tan theta = B_coil / B_H). This measures current and even the horizontal component of Earth’s field.
The science
A circular coil of N turns and radius r carrying current I produces a field at its centre B = mu0 N I / (2 r), directed along the axis. If the coil plane is set along magnetic north-south, this field is at right angles to the horizontal component of Earth’s field B_H, and the compass settles along the resultant at an angle theta where tan theta = B / B_H. So tan theta is directly proportional to I, which makes the device a current meter. If N, r and I are known, the slope of the tan theta against I graph gives B_H, the horizontal component of Earth’s field, typically around 0.3 to 0.4 gauss in India.
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 cardboard ring or plastic lid about 15 cm across for the coil frame
- About 15 m of enamelled copper wire for 20 to 30 turns
- A plotting compass with a degree scale, or a small compass placed on a printed protractor
- Resistors of 22, 47, 100 and 220 ohm
- Two AA cells in a holder and a switch
- A multimeter on milliamps
- A wooden base and a spirit level or a smartphone level app
Safety
For this project: Cells only, and keep the current below about 100 mA so the coil stays cool. Keep steel objects and phones well away from the compass during readings.
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.
All the safety rulesStep by step
8 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.
Wind 20 turns neatly around the ring, measure the mean radius of the coil, and tape the turns in place with the two ends free.
Mount the ring vertically on the base, set the compass exactly at its centre, and level the base.
With no current, rotate the whole base until the coil plane lies along the compass needle, so the needle reads zero on the scale.
Connect the cells, the 220 ohm resistor, the switch, the coil and the meter in series; close the switch and read the deflection on both sides, averaging them.
Repeat for 100, 47 and 22 ohm to get a range of currents, and also reverse the current to average out small alignment errors.
Record a table with columns for resistor, current in milliamps, theta left, theta right, mean theta, and tan theta.
Plot tan theta against I; the points should lie on a straight line through the origin.
Calculate B_H = mu0 N I / (2 r tan theta) from the slope with mu0 = 4 pi x 10^-7 and compare with the accepted value for your region.
What you should see
Deflections from a few degrees to about 60 degrees, a straight tan theta against I line, and a value of the horizontal component of Earth’s field in the range 0.25 to 0.45 gauss (25 to 45 microtesla).
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why is the coil set in the magnetic meridian?
So the coil field and Earth’s horizontal field are at right angles and tan theta = B / B_H holds.
2Why is the device called a tangent galvanometer?
Because the current is proportional to the tangent of the deflection angle, not the angle itself.
3Why read both sides and average?
To cancel small errors in centring the compass and in setting the coil plane.
4What is the field at the centre of a circular coil?
B = mu0 N I / (2 r).
Take it further
Repeat with 10 and 40 turns and show the slope changes in proportion to N.
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.
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