conclude that the magnetic field vector must point away from you, which is how it is
depicted in the diagram.
In the setup shown here, if a negatively charged electron is moving too fast, the force
exerted by the magnetic field will be greater than that exerted by the electric field, and
as a result it will pull it down. If the electron is moving too slowly, the electric field will
win the contest and pull it up. The example problem to the right shows how to determine
the strength of the magnetic field that permits an electron moving at 53,000 m/s to pass
undeflected through a uniform electric field with a magnitude of 4.0 N/C.
It is worth emphasizing that the name of the device is a velocity selector, not a speed
selector. Direction matters. You may want to consider what magnetic force would be
exerted on a charged particle that was moving horizontally, but from right to left as it
passed through the selector at the critical speed. Would the magnetic force still cancel
out the electric force?
At equilibrium:
FE + FB = 0, so |q|Eí |q|vB = 0, and
FE = force of electric field
FB = force of magnetic field
q= charge, v = speed of charge
E = electric field strength
B = magnetic field strength
This electron passes through the
velocity selector with its velocity
unchanged. What is B?
v = E/B
B = E/v
B = (4.0×10^3 N/C)/(5.3×10^4 m/s)
B = 0.075 T
28.13 - Circular motion of particles in magnetic fields
When the velocity of a charged particle is perpendicular to a uniform magnetic field, it
causes the particle to move in a circular path. In this section we discuss why this
occurs, and we state some properties of that motion.
At the right is a diagram showing a magnetic field (pointing directly into the screen) and
a positively charged particle moving in a circular path. Its motion started when the
particle was fired into the field along the surface of the page.
Why is the motion circular? First, recall that the magnetic force is always perpendicular
to the velocity vector. This means it neither increases nor decreases the speed of the
particle. It only changes the direction of its motion.
The force always points toward the center of the circle. You can use the right-hand rule
at any point of the circle to confirm this. (The fingers wrap from v to B, so the thumb
points toward the center.)
The magnitude of the force is constant. The quantities that determine the force, q,v,B,
and ș, do not change as the particle moves. Even as the particle’s velocity changes
direction, the angle șbetween the velocity and magnetic field stays constant at 90°.
Circular motion
Velocity perpendicular to magnetic field
·Force perpendicular to velocity
·Magnitude of force constant