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Magnetism
Magnetic Force
Magnetic Force
• The magnetic field is defined from the Lorentz Force Law,
BvqEqF
Magnetic Force
• The magnetic field is defined from the Lorentz Force Law,
• Specifically, for a particle with charge q moving through a field B with a velocity v,
• That is q times the cross product of v and B.
BvqEqF
BvqF
Magnetic Force
• The cross product may be rewritten so that,
• The angle is measured from the direction of the velocity to the magnetic field .
sinvBqF
v
B
v x B
B
v
Magnetic Force
Magnetic Force
• The diagrams show the direction of the force acting on a positive charge.
• The force acting on a negative charge is in the opposite direction.
+
-
v
F
F
B
Bv
Magnetic Force
• The direction of the force F acting on a charged particle moving with velocity vthrough a magnetic field B is always perpendicular to v and B.
Magnetic Force
• The SI unit for B is the tesla (T) newton per coulomb-meter per second and follows from the before mentioned equation .
• 1 tesla = 1 N/(Cm/s)B
vq
F
sin
Magnetic Field Lines
• Magnetic field lines are used to represent the magnetic field, similar to electric field lines to represent the electric field.
• The magnetic field for various magnets are shown on the next slide.
We can define the magnetic field B (a vector quantity) at a point by the vector
force Fmag at that point experienced by a particle with charge q and velocity v:
Lorentz Force Law
Fmag q v B
If there is also an electric field E at this point, then in addition
to the above magnetic force, there will be an electric force Felec=qE
and the total force Ftot on the charge will be
Ftot = Felec Fmag q E q vB
q E vB
Ph 2B Lectures by George M. Fuller, UCSD
The (vector) magnetic force on the charge q
at a particular point in space depends on the (vector) velocity of the charge and
on the (vector) magnetic field at this point:
Fmag q v B
The magnitude of this force is
Fmag Fmag q v B sin qvB sin
where is the angle between the velocity
vector v and the magnetic field vector B at this
point in space
Ph 2B Lectures by George M. Fuller, UCSD
What about the direction of the force?
Since the force is given by the vector cross product of velocity and
magnetic field, it is orthogonal to both of these. That is, the force vector will
be perpendicular to the plane defined by the velocity and magnetic field
vectors.
Fmag
v
B
Fmag q v B
Fmag Fmag q v B sin qvB sin
Ph 2B Lectures by George M. Fuller, UCSD
Consider the motion of a charged particle in a uniform magnetic field.
Let us take the case where the particle’s velocity is in the plane of the screen
and the uniform magnetic field points out of the screen:
B-field
(tips of arrows)
v
Fmag
v
Fmag
Result: uniform circular motion
In this case, we have uniform circular motion with the centripetal acceleration
supplied by the magnetic force:
Fmag qvB sin qvB sin90 qvB
Fcentrip m v 2
r
v
Fmagr
where r is the radius
of the circular path
Fmag Fcentrip
qvBm v 2
r
r m v
qB
Ph 2B Lectures by George M. Fuller, UCSD
