How to Find Magnetic Flux - Straight wire next to a loop

This is a classic type of problem, where a current in a straight wire is next to a rectangular loop, and we need to find the total magnetic flux through the loop. We need to break the loop into skinny strips of area, and find the flux through those skinny strips, then add them all up, i.e. integrate! Check it out to remind yourself.

How to Apply Ampere's Law

Ampere's law is to magnetic fields as Gauss's law is to electric fields. We only use it in 3 cases, just like Gauss, and it even looks similar to Gauss's law, only it is a 1-D integral compared to a 2-D integral. A line integral, or to some a path integral, basically means we are looking for the magnetic field times the length of the path the B-field follows. This can work for us with long, straight wires with current, a solenoid, and a toroid. Check out how to apply Ampere's law in 2 of the 3 cases, those being a straight wire and toroid.

How to Find Magnetic Forces Between Current Carrying Wires

Many electronic devices have parallel wires with currents flowing. Now, each current produces magnetic fields that circulate around the current, and these magnetic fields interact with the other current to produce a force, due to F = Il x B. Check out this video to see how to combine a couple concepts - Ampere's law determines the strength of the magnetic field from one of the currents, and then this goes into the force equation to determine the strength of the force. The right hand rule will help determine the direction of the force. Net result is that currents in the same direction attract, and in opposite directions repel. Hope this helps!