Describe the effects of a magnetic force on a current-carrying conductor.
Calculate the magnetic force on a current-carrying conductor.
Because charges ordinarily cannot escape a conductor, the magnetic force on charges moving in a conductor is transmitted to the conductor itself.
The maximum force on a current-carrying conductor occurs when the current direction and the magnetic field's direction are perpendicular to one another (i.e. ninety degree angle between directions). We can derive an expression for the maximum magnetic force on a current by taking a sum of the magnetic forces on individual charges. (The forces add because they are in the same direction.) The force on an individual charge moving at the drift velocity vd is given by
. Taking B to be uniform over a length of wire
and zero elsewhere, the total magnetic force on the wire is then
, where
is the number of charge carriers in the section of wire of length l. Now,
, where
is the number of charge carriers per unit volume and
is the volume of wire in the field. Noting that
, where
is the cross-sectional area of the wire, then the force on the wire is
. Gathering terms,
Because
,
is the equation for
maximum magnetic force on a length
of wire carrying a current
in a uniform magnetic field
, as shown in
[link] .
If we divide both sides of this expression by
, we find that the magnetic force per unit length of wire in a uniform field is
The direction of this force is given by RHR-1, with the thumb in the direction of the current
. Then, with the fingers in the direction of
, a perpendicular to the palm points in the direction of
, as in
[link] .
Calculating magnetic force on a current-carrying wire: a strong magnetic field
Calculate the force on the wire shown in
[link] , given
,
, and
.
Strategy
The force can be found with the given information by using
because the angle between
and
is 90
.
Solution
Entering the given values into
yields
The units for tesla are
; thus,
Discussion
This large magnetic field creates a significant force on a small length of wire.
Magnetic force on current-carrying conductors is used to convert electric energy to work. (Motors are a prime example—they employ loops of wire and are considered in the next section.) Magnetohydrodynamics (MHD) is the technical name given to a clever application where magnetic force pumps fluids without moving mechanical parts. (See
[link] .)
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