Question

3. A piece of wire 2 cm long is inside a solenoid with 2000 turns/m. The table shows a measurement of the force exerted on the wire as a function of the current through the solenoid. According to our lab notes, the force should satisfy F- I f B and the magnetic field should be given by B-4 (NL) I Plot the data and determine if these equations describe the experiment properly. If the model is correct, determine the value of o 0.0 0.15 0.65 1,47 2.53 4,04 0.0 10

Answer 1

The magnetic force on the small piece of wire is:

F = BILsin90 = BIL

where B = magnetic field due to the solenoid which is: $B=\mu_o (N/l)I$

so, $F=\mu_o nI^2L$

where n = 2000 turns/m and L = 2cm = 0.02 m

=> $F=40\mu_o I^2$

this is of the form: y = ax²

so, the graph of Force vs current will be an upward parabola.

The data given above does not support this force-current trend as it does not give an accurate value of permeability of free-space which is $\mu_o = 4\pi \times 10^{-7} =1.2566\times 10^{-6}Tm/A$ .