A magnetic field exerts a force on a charged particle that is perpendicular to both the velocity of the particle
and the direction of the magnetic field. The Lorentz force is a cross product, and so obeys the right-hand rule.
A simple motor can illustrate the effect of the Lorentz force.
Can you explain what makes this work?
Sample questions
1. What would be the direction of the force exerted on a proton moving as shown, by this magnetic field?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
2. What would be the direction of the force exerted on a proton moving as shown, by this magnetic field?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
3. What would be the direction of the force exerted on an electron moving as shown, by this magnetic field?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
4. What would be the direction of the force exerted on a proton moving as shown, by this magnetic field?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
5. What would be the direction of the force exerted on a proton moving as shown, by this magnetic field?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
Cyclotron motion
A charged particle moving in a plane perpendicular to a magnetic field feels a Lorentz force.
The Lorentz force is always perpendicular to the velocity, so it constantly deflects the particle sideways.
The particle moves in a circle at constant velocity. The force is pointed radially inward.
Since the force is perpendicular to the velocity, we can simply write the force as qvB, and relate it to centripetal force.
This allows us to easily find the radius of the circular path of a particle, and its frequency.
The radius and frequency depend on the ratio q/m, which is a good identifier for a specific type of particle.
Measuring the radius or frequency of a praticle in a cyclotron is a powerful tool in studying atomic and subatomic particles.
If the velocity of the particle also has a component parallel to the magnetic field, it will move in a spiral pattern.
Check out this website
for an interactive simulation of 3-D charged particle motion in a magnetic field.
Sample question
1. What is the speed of a proton moving in a circle of radius 2.45 cm in a magnetic field of magnitude 125 mT?
Assume the plane of the circle is perpendicular to the magnetic field.
Proton mass = 1.67 x 10-27kg, proton charge = 1.60 x 10 -19C.
Magnetic forces on current-carrying wires
We can easily derive the formula for the magnetic force on a length l of a current-carrying wire from the Biot Savart law
using the drift velocity over a length of wire. The length vector has the same direction as the positive current flow.
Sample questions
1. What is the direction of the net magnetic force on wire B from wire A?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
G. the net force is zero
2. What is the direction of the net magnetic force on wire A from wire B?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
G. the net force is zero
3. What is the direction of the net torque on wire A from wire B?
A. up
B. down
C. right
D. left
E. into the page
F. out of the page
G. the net torque is zero
4. Consider two long parallel wires carrying current as shown.
At what point or points on the x-axis does the magnetic field equal zero?
