Answer Happy

Table 2 Calculated values of constant C, B, (with units) and percentage error Measurement C % error В. #1 #2 #3

Table 1 Fitting parameters (with units) from the info-boxes in the graph Measurement Slope Intercept #1 (North-1) 6202 #2 (North-2 #3 (North-3) COTZ North I 10.501 O. 15 16 9,8339 10.168 0.1531 North 2 North 3 0,1701

27 11 ) (6) 7 m B=CB, with C= (5) 724/ 41 T is the period of the oscillation. The constant C depends on the magnetic moment and the moment of inertia of the bar magnet, which is unknown. Hence, in order to obtain the horizontal component of the earth's field, we must first find C for the bar magnet, i.e., we must calibrate it in a known uniform magnetic field. In this experiment the known uniform magnetic field is produced by Helmholtz coils consisting two identical coils separated by a distance equal to their radius. The two coils carry the same current in a direction such that, at the midpoint between them on their axis, their magnetic field will have the same direction and the same magnitude, so the magnitude of the total magnetic field at that point is (4) Nuc 0.72N MIC B= R R N is the total # of turns of each Helmholtz coil, R is the radius of Helmholtz coil, Ic is the DC current going through each Helmholtz coil, 4o = 47x10- T.m/A. The SI units (international system of units) of the magnetic field is T (Tesla). The Gaussian units of the magnetic field is G (Gauss). 1 T = 10000 G. If we align the Helmholtz coils so that its axis is in the same direction as B. , the horizontal component 0.72N Holc of the earth's magnetic field, the fields add to give a total magnetic field Bor = B. + and R equation (5) becomes 1 12 + =CB, +C R R This equation shows how we can find the constant and determine the magnetic field B. We cannot obtain C from a single measurement because both C and B, are unknown. We must measure the period of oscillation T for various values of the current / through the coils. The plot of -1 versus Ic will be T2 straight line with a slope C .0.72NH and an intercept CB, from whieh the values of C and B, can be R determined since the Helmholtz coils used in this experiment with N=200 turns, R=10.5 cm. =C СВия cB =C(2, 4 0.72N/6/2 „0.72N440) (7) -Ic