Simple Experiments to show
the magnetic field due to a current
in a single turn.

See Solenoid

I constructed a wooden frame to hold a single turn 50 cm in diameter of 16 gauge (1.6mm) tinned copper wire.  A resistor of ten ohms and a switch were placed in series.  A regulated power supply unit supplied 20 volts giving a current of 2 amps.

The diameter of the loop was lined up with the horizontal component of the Earth's field at that point.   Measurements were taken at 5 cm intervals across the diameter with the centre as one of the points.  At each point the deflection of the magnetic compass due to the current was measured as an angle from magnetic north. 

Theory:

The angle the compass takes up is along the direction of the vector sum of the Earths Field and the field due to the current in the loop.

Text Box: Tan (Theta)=M/E
So M=E Tan (Theta)

Photograph of Apparatus:

Results:

Distance from centre (cm) Deflection (degrees) Tan (deflection)
-20 30 0.577
-15 20 0.364
-10 16 0.287
-5 15 0.268
0 14 0.249
5 14 0.249
10 16 0.287
15 20 0.364
20 30 0.577

Conclusion:

The field is not uniform across the diameter but rises towards the wire.  Gauss's construction of magnetic shells predicts that the magnetic field due to a current loop is constant across its diameter.  The results obtained may be due to errors caused by the very thin nature of the shell and the difficulty of keeping the compass within it.

Comment:

I did this experiment because I wanted to test a calculation I had done using the Biot-Savart hypothesis to find the off-axis magnetic field of a single turn.  My experimental results supported my calculations and I am surprised this has not been pointed out in physics textbooks before.

I think that this demonstration should be carried out at school as part of the elementary general physics course

I repeated this experiment with another loop and got a similar result.

 

The results obtained with the single turn together with the results of the solenoid I come to the conclusion that a single turn gives a different result from a solenoid.

 

This indicates that magnetism is not the phenomena that philosophers thought is was for 300 years since Gauss.

 

The "magnetic" effect of current does not exist the force between current carrying conductors is a relativistic phenomena due to length contraction visible between relatively moving charged particles.

To analyse the forces on a bar magnet a different analysis must be used as the iron's magnetism is due to electron spin and the force is between these "current loops" and the electrons in the wire moving relative to the fixed positive charges in the wire.

The other force is due to the currents in the molten core of the earth and ionosphere and our simple idea of magnetism does not fully model what is happening.

This resultant angle of rest (the angle the bar magnet points) is the result of these interaction and may be strongly related to quantum mechanics as well as relativity.