Commons

except that the bottom charge is now the opposite type. This turnsthe attraction into a repulsion. (We know that flipping the chargereverses the interaction, because that’s the way it works for electricforces, and magnetic forces are just electric forces viewed in adifferent frame of reference.)A magnetic weathervane placed near a current. example 1Figure n shows a magnetic weathervane, consisting of two chargesthat spin in circles around the axis of the arrow. (The magneticfield doesn’t cause them to spin; a motor is needed to get them tospin in the first place.) Just like the magnetic compass in figure h,the weathervane’s arrow tends to align itself in the direction perpendicularto the wire. This is its preferred orientation becausethe charge close to the wire is attracted to the wire, while thecharge far from the wire is repelled by it.Magnetic fieldsHow should we define the magnetic field? When two objects attracteach other gravitationally, their gravitational energy dependsonly on the distance between them, and it seems intuitively reasonablethat we define the gravitational field arrows like a street signthat says “this way to lower gravitational energy.” The same ideaworks fine for the electric field. But what if two charged particlesare interacting magnetically? Their interaction doesn’t just dependon the distance, but also on their motions.We need some way to pick out some direction in space, so wecan say, “this is the direction of the magnetic field around here.” Anatural and simple method is to define the magnetic field’s directionaccording to the direction a compass points. Starting from thisdefinition we can, for example, do experiments to show that themagnetic field of a current-carrying wire forms a circular pattern, o.But is this the right definition? Unlike the definitions of thegravitational and electric fields’ directions, it involves a particularhuman-constructed tool. However, compare figure h on page 117with figure n on page 121. Note that both of these tools line themselvesup along a line that’s perpendicular to the wire. In fact, nomatter how hard you try, you will never be able to invent any otherelectromagnetic device that will align itself with any other line. Allyou can do is make one that points in exactly the opposite direction,but along the same line. For instance, you could use paint to reversethe colors that label the ends of the magnetic compass needle, oryou could build a weathervane just like figure n, but spinning like aleft-handed screw instead of a right-handed one. The weathervaneand the compass aren’t even as different as they appear. Figure pshows their hidden similarities.n / Example 1o / The magnetic field curlsaround the wire in circles. Ateach point in space, the magneticcompass shows the direction ofthe field.Nature is trying to tell us something: there really is somethingSection 6.2 Electromagnetism 121