Download Magnetic Fields and Forces

Magnetic Fields and Forces
Notes Sheet
1. Magnetic fields from a bar magnet
The picture top left shows the familiar pattern of magnetic fields from a permanent bar magnet.
2. Magnetic fields from Long Straight Wire:
The magnetic field direction around a long straight wire is given by a right hand rule as shown
by the image top right. Notice that the fields circle around the wire and get weaker at distances
farther from the wire. The equation
B=
μo I
2πr
where B is the magnetic field in units of Tesla, µo = 1.26 x 10-6 T·m/A , I is current in Amps, and
r is the distance outward from the wire in units of meters.
3. Magnetic fields from a long solenoid :
The magnetic field is concentrated into a nearly uniform field at the
center of the coil. The field outside is weaker and loops back as shown.
The direction of the field in the center is given by another right hand rule
where the fingers of the right hand are curled in the direction of the
current in the coils and the thumb points in the direction of the magnetic
field within the solenoid. The equation for the magnetic field in the
interior of the solenoid is given by the equation
B = μo n I
where n is the number of turns per unit length and I is the current through
the coil. Magnetic fields from a more loosely wrapped coil might be
represented by the image at the right.
4. Force from charges moving through a magnetic field:
The diagram at the right gives two
versions of the right hand rule for
determining the direction of the force on
a charged particle moving through a
magnetic field. It should be emphasized
that


The force is perpendicular to both
the velocity v of the charge q and the
magnetic field B.
The magnitude of the force is
maximized when the direction of the
velocity and the magnetic field are
perpendicular to each other.

The magnitude of the force for more general circumstances is given by the equation
F = qvB sinθ
where θ is the angle between the velocity and the magnetic field, q is the charge on the
moving particle, v is the velocity, and B is the magnetic field. This equation correctly states
that the magnetic force on a stationary charge or a charge moving parallel to the magnetic
field is zero.

The force for the preferred orientation of magnetic field and velocity being perpendicular to
each other is given by the equation
F=qvB
5. Force on a wire carrying current in a magnetic field
Since a wire carrying current is equivalent to
charges moving through the wire, there is a
magnetic force on these moving charges as
well. In this discussion we consider
conventional (not electron) current flow.
The equation for the force on a wire of
length L in a magnetic field B is
F=ILB
It should be clear that it is not the total
length of a wire that goes into the equation
above but rather the portion in the magnetic
field. The diagram to the right shows the
similarity between charges moving through
a wire and in a vacuum.
6. Memory aid for force equations:
Since the charge on an electron is given the symbol e, having a value of 1.6 x 10-19 Coulomb,
students have used the following memory aid to help remember the two equations above. In
the memory aid, the equations the force is equal to the sweethearts Bev and Bil. Maybe it
helps.
F = Bev
&
F = Bil
7. Force between two wires carrying current:
There are many examples of a wire carrying current in the neighborhood
of other current carrying wires and interacting through the mechanism of
magnetic fields. The simplest example is two long straight wires
separated by a distance. In this example we are interested only in the
direction of the forces and will not give the force equation. If we consider
wire 1 carrying current I1 producing a magnetic field at the location of
wire 2 into the page, the right hand rule at that point indicated a force
toward the first wire. Considering wire 2 as the source of magnetic fields
leads to an attractive force relationship between the two wires.