29.8-29.10
We have seen that a moving charge feels a magnetic force. Since a current in a
wire is just a large number of moving charges we can rewrite the magnetic
force for wires with currents.
A little bit of algebra and one goes from
\vec{F}_{point \; charge} = q\vec{v}\times\vec{B}
to
\vec{F}_{wire} = I\vec{l}\times \vec{B}
Again the cross product and RHR. Practice, practice, and practice some more to master it. Note also
that l is the length of the (straight) piece of wire and the direction is
given by the direction of the current.
The two examples 29.13 and 29.14 in the book are good to look at. Eq 29.27 is
for the force between two wires. The idea there is that you combine the
magnetic field produces by 1 wire with the magnetic force formula.
So wires that are near each other will attract if they have current in the
same direction and repulse with opposite currents. Make sure you understand
why the repulsion/attraction.
Torque on Coil.
In a coil, the current is in opposite directions in each side. The magnetic
field will thus create opposite forces and there will be a torque with respect
to a pivot at the center of the coil.
In the video, I make a mistake and write the unit vector
\hat l
. The formula really involves the length vector
\vec{l}
(but for a curved loop, you should only talk
about the force on a small segment approximately straight.)
The book derives the formula for torque on a coil in the case of a square
loop. This formula turns out to be valid for any loop shape.
\vec{\tau}=\vec{\mu}\times\vec{B}
I think it is important to read the last section (29.10) of the book to close
the loop and the return to the first magnets we saw, the natural permanent
magnet (the bar magnet). Technically, this reading is optional though and we will
not have questions about it. It is surprising how complex natural permanent
magnets are and this chapter does a very good job of giving you the basic
ideas of a subject that is usually reserved for more advanced physics classes.