Magnetic Force on Current-Carrying Wires
Since an electric current is just a bunch of moving charges,
wires carrying current will be subject to a force when in a magnetic
field. When dealing with a current in a wire, we obviously can’t
use units of q and v.
However, qv can equally be expressed
in terms of Il, where I is
the current in a wire, and l is the length, in
meters, of the wire—both qv and Il are expressed
in units of C · m/s. So we can reformulate the equation for the
magnitude of a magnetic force in order to apply it to a current-carrying
wire:
In this formulation,
is the angle the wire
makes with the magnetic field. We determine the direction of the
force by using the right-hand rule between the direction of the
current and that of the magnetic field.
Example
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In
the figure above, a magnetic field of  T is applied locally to one part of an
electric circuit with a 5  resistor and a voltage of 30 V. The length
of wire to which the magnetic field is applied is 2 m. What is the
magnetic force acting on that stretch of wire? |
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We are only interested in the stretch of wire on the right,
where the current flows in a downward direction. The direction of
current is perpendicular to the magnetic field, which is directed
into the page, so we know the magnetic force will have a magnitude
of F = IlB, and
will be directed to the right.
We have been told the magnetic field strength and the
length of the wire, but we need to calculate the current in the
wire. We know the circuit has a voltage of
30 V and
a resistance of
5 
, so calculating the current
is just a matter of applying Ohm’s Law:
Now that we know the current, we can simply plug numbers
into the equation for the force of a magnetic field on a current-carrying
wire:
