We've compared Ampere's law to Gauss's law, where it is a way to figure out what magnetic fields are doing for our three shapes. For those shapes the math reduces down to just figuring out the length of the path the magnetic field follows. The obvious question then becomes, what happens for everything else that is not one of the three shapes? Just like in electricity, where we had to move on to the NON-Gauss integrals, now we will need to move to the NON-Ampere situations, such as real wires that do have ends.
The general way to find magnetic fields is called the Biot-Savart rule; for us, it's just B-S.
Check out B-S for single particles that are moving. Then, check out current moving in a straight wire with ends. There is a B-S video for loops of current, as well as multiple wires and finding total B-fields. Note that current densities (uniform and NON-uniform) are used if we need to find B-fields inside wires.
To visualize B-fields for all sorts of situations, there are some wonderful 3-D simulations!
Try Ch. 28 #8 (p. 11). Use the picture and values in Ch. 28 #72, to find the overall magnetic field at a point 10 cm below the bottom section of the loop, on the line that bisects the top and bottom parts of the loop...find the three magnetic fields from the long wire and the top and bottom sections of the loop and their directions. By Friday, we'll also have an article summary (forms on front desk) of your choice.
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