Force on a Moving Charge
A charged particle experiences a force when moving at a non-zero angle
with respect to a magnetic field. The force on the charge is greatest when
It moves perpendicular to the magnetic field.
F=qvB sinθ
q = the amount of charge in motion in the magnetic field
v = the velocity the charge in the magnetic field
B = the magnetic field strength
θ = the angle between the velocity direction and magnetic field
•The force, charge velocity direction, and magnetic field direction are all perpendicular to each other.
• There is no force on a charge that moves parallel to a magnetic field.
Direction conventions:
•: out of the page (+z)
x: into the page (-z)
B
B
Field lines out
of the page
x x x
v
x x x
x x x
Field lines
into the page
velocity out
of the page
F
x
force into
the page
First Right Hand Rule
• Used to determine the velocity direction, force direction, and
magnetic field direction for a charge in motion in a magnetic field.
• The right hand rule is used for positive charges.
force
velocity
magnetic field
Example Problem
• A proton moves at 3.0x105 m/s in the
positive-x direction while a 4.5 T magnetic
field acts in the negative-y direction. What
is the magnitude and direction of the force
exerted on the proton?
F=qvBsinθ=(1.6x10-19C)(3.0x105 m/s)(4.5 T) sin90°=2.2x10-13 N
• Use the first right hand rule to determine the force
direction on the charge.
• -z direction
What is the resulting motion of a
charge in a magnetic field?
v
F
What is the direction of the magnetic field surrounding the charge?
Force on wire in a magnetic field
A current in a wire constitutes charges in motion.
+
+
+
+
+
+
+
I
L
F = qvBsinθ =q(L/t)B sinθ = (q/t)LBsinθ = BILsinθ
F=BILsinθ
F=force on the wire from the external magnetic field
B = The external magnetic field that surrounds the wire
I = current in the wire
L=length of wire in the magnetic field
θ = angle between the current direction and magnetic field.
The direction of the magnetic field can be determined by the right hand rule with
the current I, replacing the velocity direction.
Example problem
• A wire length carries 6.5 A of current along the positive-x
axis while in a magnetic field of 7.0 T directed towards
the positve-z axis. A length of 18 cm of wire is exposed
to the magnetic field. What is the magnitude and
direction of the force on the wire?
• F=BILsinθ = (7.0 T)(6.5 A)(.18m)sin 90°
• F=8.2 N
• Use the right hand rule to determine the direction of the
force.
• Force direction: -y
An Applications of Force on a Wire –
Simple Internal Diagram of an Electric Motor
Motor – a device which converts energy to mechanical motion
Metal brushes
inside ring
S
I
I
x
•
N