Experiment 2

Experiment 2.10 THE MAGNETIC FIELD

ANALYSIS

From equation (2) we see that the magnitude of the total magnetic field present at the position of the jar magnet is given by:

(3)

where c is a constant of proportionality, which when known serves to provide a calibration of the magnitude of the magnetic field in terms of the period of the jar magnet. The magnetic field in tesla (T) produced by the Helmholtz coils is:

(4)

where N is the number of turns per coil, R is the radius (in meters) of each coil, and I is the current (in amperes) through the coils. Combining equations (3) and (4), we find:

(5)

where B_eis the magnetic field of the Earth.

1. In equationn (4) above, using the physical characteristics of the Helmholtz coils, calculate the proportionality constant k between the Helmholtz coils’ magnetic field and the current that produces it.

k = (9.0 X 10^-7 T-m/A) N/R

where N is the number of turns per coil and R is the radius (in meters) of each coil.
Enter the result in cell D68.

2. Make a new column on the right side of the data table in cells E45:E49 for values of 1/T². In cell E45 enter: "= 1/D45^2 ". Then use EDIT...Fill Down to complete the data column.
3. Plot against I by first selecting the current column (B45:B49). Then, with the Apple key down, select the E45:E49 column.

Use the Excel Chart Maker to make this plot.

Select the x-y scatter icon

from the top Toolbar.

Click on the chart itself.

Click on the legend and hit Delete.

From the View menu, select the Formatting Palette if it is not already present.

Select Chart Title from the Title pull-down menu and fill it in.

Next select titles for the Horizontal and Vertical axes and fill them in.

Use the mouse to size the chart and to locate it below the data on the Worksheet.

3. Click on any one of the data points.

Choose Chart...Add Trendline from the menu.
Under the Options tab, choose Display equation on chart. The equation of the best straight line fit to the data will appear on the chart. Move it to the top header of the plot to make it readable.

4. Record the slope s in cell D70 of the Worksheet. Using this value and the value obtained for the proportionality constant k, compute:

(6)

Record the value of the calibration constant c in cell D72. The jar magnet is now calibrated so that the magnitude of a magnetic field in which it is placed can be determined directly from the period of oscillation by using equation (3).

5. Compute the period of the Earth’s field measurement, and record the value in cell D64. Use equation (3) to calculate the magnitude of the horizontal component of the Earth's magnetic field and enter the result in cell D74. Compare the measured value with the value listed for your location in a handbook of physical measurements and compute the percentage error in cell D76.

6. Answer Questions 1 and 2 on the Worksheet and use it to develop your lab report.