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Magnetic Field Shapes
 Magnetic fields are represented by magnetic lines of force. A magnetic line of force is a line showing the direction of the force which would act on a free north magnetic pole placed at the point. However, since you never usually find a north pole without a south pole nearby, you might prefer to think of the lines as showing the direction in which a tiny compass would point when placed in the field. Magnetic Field Produced by Current Flowing in a Long Straight Conductor It is observed that the magnetic field lines around a long straight current-carrying conductor are circular. Notice that the diagram here shows what is called conventional current, imagined to flow from the positive of the supply to the negative. This is for "historical reasons". For more detail on this... look somewhere else... I can't be bothered discussing this any more! Actual electron flow in metals is, of course, the other way. This will be the case in all work on magnetic fields. In order to put arrows on the lines of force, some memory aids have evolved. This one is for any wine lovers out there. Imagine a "normal" corkscrew. In order for the screw to go into the cork you must turn the screw clockwise (from the wine lover's point of view). The relation between the sense of the flow of current and the sense of the arrows on the lines of magnetic force is the same as those associated with the action of the corkscrew. The "corkscrew rule", above, reminds us that the arrows on the lines of magnetic force should be as shown in this diagram. Magnetic Fields Produced by Currents Flowing in Two Long Straight Parallel Conductors Field Produced by Currents Flowing in the Same Sense The orange circles represent the ends of the conductors (for example, they could be the end view of two pieces of copper wire). In diagrams of magnetic field shapes we often need to indicate the sense of a current flowing into or out of the plane of the diagram, as is the case here. We will use the convention that a cross like this × means current flowing into the plane and a dot ● (as in the next diagram) means out of the plane of the diagram. Somewhere on a line joining the centres of the two conductors there will be neutral point (that is, a point where the magnetic field strength is zero. This will be at the mid point if the currents are of equal magnitude. At points very close to either conductor the lines are very nearly circular. If we move very far from the two conductors (compared with the distance between them) we will begin to see circular field lines again. It is observed that the electro-magnetic forces between two conductors like these cause them to attract each other. Field Produced by Currents Flowing in Opposite Senses In this case the conductors are found to repel each other. Both the repulsion here and the attraction in the previous case are weak forces unless the currents are very strong and/or the distance between the conductors is very small. A short coil of wire carrying a current also produces, in a plane parallel to the central axis of the coil, a field of similar shape to that shown above. Diagram on the left, below. Two identical  short coils separated by a distance equal to their radius can be used to produce a (nearly) uniform field in the central region (as indicated by approximately constant "density" of lines), see diagram below, right. This arrangement is described as a pair of Helmholtz coils. Magnetic Field due to a Long Coil (Solenoid) Another way to obtain a uniform magnetic field strength is by using a long uniformly distributed coil of wire, often called a solenoid (pronounced solenoid). This has the advantage that it can produce a very nearly uniform field over a rather larger volume than using the Helmholtz coils but with the disadvantage that the field is inside the coil and therefore somewhat inaccessible for some purposes. It is found that if the length of the solenoid is 10 times its radius (or diameter or something... look it up for yourself) then the region of uniform field can covers around 95% of the space inside it. This field has pretty much the same shape as that of a bar magnet and for that reason is sometimes considered to have magnetic poles. Another aid to memory: Imagine looking at one end of the solenoid (from the outside). Imagine also that you can see conventional current flowing (ok, I know this is beginning to sound a bit imaginary, but still...) If the current flows clockwise, from your point of view, then that end of the solenoid will behave like a south pole... and how do you remember that ? Look at the letter S, below, with clockwise arrows on it! Same logic for the other end; conventional current counter clockwise, see the letter N below. After having decided on the N and S pole positions you can add arrows to the lines remembering that the lines go away from N towards S (outside the magnet). You can also use the corkscrew rule if you prefer or one of quite a few others not mentioned here...
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