Magnet Deflection Example

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Magnet Deflection Example

This example fits a function involving an arc tangent and a variable to the third power. This is an interesting physics problem. If a magnet is placed due east of a compass, the deflection of the compass needle from north is equal to the arc tangent of the ratio of the strength of the magnet's field relative to the earth's magnetic field. The strength of the magnet's field at the compass is inversely proportional to the cube of the distance from the magnet to the compass. Thus, the function relating these terms is

 Deflection = atan(Strength / Distance ^ 3)

The deg() function converts an angle in radians to degrees. In the example, Deflection and Distance are the variables, and the value of the Strength parameter is determined.

Title "Deflection of compass due to magnet east of it";
Variable Distance;              // Distance of magnet from compass (inches)
Variable Deflection;            // Deflection in degrees
Parameter Strength;             // Strength of magnet
Function Deflection = atan(Strength / Distance ^ 3);
Plot xlabel="Distance from compass (cm)",ylabel="Deflection of compass";
Tolerance 1E-7;                 // Specify convergence criterion
Data;
[ data goes here ]