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magnet test 03.05.23

00007: Helmholtz Coil

Step	Step description	Expected Result	Result
Precondition	System is Off
Switch On the system	Turn On the Helmholtz Coil by providing it with an power supply (P3) equal to 21.7 V	Get magnetic field ( B= 0.01 T)	positive
Switch Off the system	Turn Off the Helmholtz Coil	Magnetic field stops	positive
Postcondition	System is Off

Analysis of the test results:

First, we place the magnetic field meter in the appropriate position (with its head in the middle between the two coils, and perpendicular to the direction of the magnetic field).

Then we started changing the voltage at each step, which thus changes the current I and the magnetic field B.

We keep increasing the U until we reach the required I, which gives us B = 0.01T.

Experimentally:

U (V)	4.55	5	6	7	8	9	9.47	10.05	12	14.33	17.46	21.7
I (A)	0.8	0.88	1.05	1.24	1.42	1.6	1.75	1.79	2.13	2.5	3	3.61
B (mT)	2.3	2.5	3	3.5	4	4.5	4.8	5.02	5.96	7.01	8.45	10
R (Ω)	5.69	5.68	5.71	5.65	5.63	5.62	5.41	5.61	5.63	5.73	5.82	6.01	Rm=5.68

Theoretically:

I (A)	0.8	0.88	1.05	1.24	1.42	1.6	1.75	1.79	2.13	2.5	3	3.61
B (mT)	2.24	2.46	2.94	3.46	3.97	4.47	4.89	5.01	5.96	6.99	8.38	10.09

The formula for the magnetic field in a Helmholtz coil is given by:

B = (μ0 * I * N * R^2) / (2 * (R^2 + (x - d/2)^2)^(3/2))

Or :

B is the magnetic field in Tesla (T)
μ0 is the magnetic permeability of vacuum, equal to 4π × 10^-7 T m/A
I is the electric current in the coil in amperes (A)
N is the number of turns in each coil
R is the radius of each coil in meters (m)
d is the distance between the two coils in meters (m)
x is the distance along the central axis of the coils in meters (m)

In our case :

N= 267

R=6*10^-2 m

x=3*10^-2 m

d=6*10^-2 m

We confirmed that the direction of the magnetic field is uniform by positioning the gauge in the same direction as the expected magnetic field;

and the result was positive (B=0)