Day 5: Interpreting Magnetic Field Maps
Magnetic fields are complex three-dimensional "structures". While field lines
have no material existence (we can't hold a field LINE in our hands), they mark
out a "guiding center" along which moving charged particles will travel while
simultaneously orbiting about the line. In general, we do not allow representations
of fields to suggest particles at a particular point have a choice of paths.
Classical physics is pure cause and effect! Thus, we never represent a static
(time-independent configuration) field of any particular kind (here, magnetic)
as having crossed field lines. A bit later in this unit, we will find that
magnetic field lines can merge (reconnection) in certain circumstances. (This is
not a static phenomena!) Reconnection is non-trivial as it helps us understand
aurora and the heating of the solar corona to over 1000 times the temperature of
the surface of the sun.
Can we provide a physical analogy or picture that explains how a non-material
field exerts a force on a material object? To provide a physical picture of the
idea of "fields" try the following activity.
Ask the students to stretch a large cloth sheet taut and level. Associate it with
the "fabric of space." Many students have heard of the "tearing of the fabric of
space" in various movies and on TV so the notion of space as a fabric or surface
may not be unfamiliar to them. Place a light ball (Ping Pong) on the sheet: It will
sit where placed. Next, roll it across the sheet. It will travel in a straight line,
exhibiting unaccelerated motion. Next place a fairly large mass (a brick or a bowling
ball) in the center of the sheet. Repeat placing the light ball on the sheet. It will
start moving toward the central mass, as if attracted by it. Repeat rolling the light
ball on the sheet. This time it follows a curved path. This is analogous to net
unbalanced, center-seeking or centripetal force acting on the object. We can associate
this generalized force with any non-contact force, like gravity, electricity, and
Some care is suggested in reminding the students that the analogy depends on our
living in a gravitational field and the gravitational interaction between earth
and bowling ball produces the dent. In the 'real space' of charged particles, the
charge of the particle is the cause of the dent, not some interaction with an
Magnetism is different from gravity or electricity because there must be relative
motion between a charged object and the observer to produce it. Further, the
direction of the magnetism is out of the plane described by the relative motion.
This can be modeled by placing a ball on the taut sheet and running a broomstick
quickly along the underside of the sheet (but not through the ball's position.)
The ball will hop out of the plane of the sheet. This is analogous to magnetism
by virtue of exhibiting the need for relative motion and for the interaction force
to produce a new motion (the hop) out of the plane of the original relative motion.
In this lesson, students will be testing their predictions of magnetic field shape
for combinations of two bar magnets. Students will be asked to try to remove the
contribution of the earth's magnetic field from their observations. The earth's
field dominates the observation far from the bar magnet field being observed. This
is an important point to dwell on. Much science consists of teasing out the signal
or evidence we are interested in from the (often) larger and obscuring background
signal we simultaneously receive with the desired observation data. An analogy is
the common teaching construction of Newton's Laws using "frictionless" situations.
The second part of the lesson plan involves the students translating the view of
the map. Instead of a top down look, students will be asked to look from different
angles and predict the shape of the field that would be seen. We will check
predictions by placing a bar magnet on end and mapping the field.
Lesson Development/Writing: Ed Eckel
Web Design: Theresa Valentine
Last Updated: 8/11/2000