Students will use a spreadsheet to calculate the magnetic field along the x-axis of a solenoid of length ls, radius R, and n turns per unit length carrying current I. The solenoid is centered at the origin with its axis along the x-axis. The field at any point x is
B = (1/2)m0nI[f1(x)-f2(x)],
where
f1(x) = (x+(1/2)ls) / [R2+(x+(1/2)ls)2]1/2
and
f2(x) = ( x-(1/2)ls) / [R2+(x-(1/2)ls)2]1/2.
(a) Let ls=10cm, R = 0.5cm I = 4A, and n = 1500 turns/m. Construct a spreadsheet that calculates B as a function of x for positive values of x ranging from x = 0 to x = 30cm in steps of 0.2cm. Plot B versus x. (Note: use SI units consistently.)
(b) Change R to the following values and observe the effects on the graph in each case: R = 0.1cm, 1cm, 2cm, 5cm, and 10cm. For small values of R (small compared to ls) the field inside the solenoid should look like that of an ideal (infinitely long) solenoid. For large values of R the field should look like that of a loop. Does it?
(c) For x >> ls (where x is measured from the center of the solenoid) the magnetic field of a finite solenoid along the x-axis approaches
B(x) = (m0 / 4p)(2m / x3)
where m = NIpR2 is the magnetic dipole moment of the solenoid. Modify your spreadsheet to calculate and plot x3B(x) as a function of x. [Multiply your column containing B by the cube of your column containing x.} Verify that x3B(x) approaches a constant for x >> ls. [Use a log scale for the y-axis. Leave out the first point since the log of zero is not defined.]
To earn extra credit, save your Excel document (your name_exm7.xls) and attach it to an e-mail message to mbreinig@utk.edu. Comment on your results.