Draw a bar magnet as if it were a magnetic dipole consisting of two "magnetic" monopoles of the same size (unit), but of opposite signs separated by a fixed distance L (the axis of the bar is called longitudinal here)
The magnetic field of a permanent magnet (I)
Prediction: Calculate the magnitude of the magnetic field as a function of the distance from one of the poles along the longitudinal axis.
Prediction method:
We are going to assume that a magnet behaves similarly to an electric dipole in order to get a mathematical model for the magnetic field. This comparison is not based on any physical theory (because we know there is no magnetic charge), but it has the advantage of allowing us to simply analyze the field of a magnet.
1. Draw a bar magnet as if it were a magnetic dipole consisting of two "magnetic" monopoles of the same size (unit), but of opposite signs separated by a fixed distance L (the axis of the bar is called longitudinal here).
2. Choose one of the monopoles as the origin of your longitudinal axis (drawn in #1). Take any point outside the bar at position d on your axis.
3. Assuming that the magnetic field behaves similarly to the electric field of a point charge, determine the direction of the magnetic field from each pole to that point (Hint: There are two "magnetic" charges, because it is a dipole.)
4. Obtain an expression for the magnitude of the magnetic field B as a function of d and L assuming that all constants (Coulomb's constant and the two "magnetic" charges) are equal to one.
5. Graph B against d.
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