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Detailed magnetic field of a wire between two opposing magnetic poles

In order to find the detailed magnetic field of a wire between two opposing magnetic poles, you have to use Fleming's left-hand rule. The thumb can then provide you with the direction of force on the wire, as can be seen below in the three diagrams.

Magnetic fields between two magnets and a wire with current flowing away from you.

 

Using Flemings left hand rule the thumb shows the direction the wire will move.

Gives

Force that acts on the wire.

Now you know the direction of the force on the wire, imagine a catapult (in UK) or slingshot (in US) with bunched up elastic bands ready to shoot in the direction of the force. This will remind you that magnetic force lines are bunched behind the wire.

Sling shot

In fact the overall detail will look like the following:

Magnetic field lines bunching up and interacting with the wires field lines.

 

If the magnets were turned around we would have the following three diagrams.

Magnetic field lines plus field lines produced by current flowing through wire.

Gives

Direction the wire will move in this magnetic field

This will mean that the magnets' field line will be more bunched below the wire and will try to sling the wire in the direction of force.

Magnetic field around a wire

 

Finally we can use these ideas when the current in the wire travels towards you rather than away from our view.

Force and direction of motion the wire takes in the magnetic field

This gives you a detailed magnetic field as follows:

Magnetic field around a wire

With the current in the wire traveling towards you but with the magnets reversed we get the following:

Force and direction of motion the wire takes in the magnetic field

This gives you a detailed magnetic field as follows:

Magnetic field around a wire

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