AP Physics C
Magnetic Field and Magnetic Force
Free Response Problems
1. An electron with a mass m and charge e is accelerated from rest through a potential difference
of magnitude V between two long parallel plates. The electron then passes into a region of
uniform magnetic field B to the right of a system of two charged plates. The magnetic field is
directed into the page.
a. On the diagram above, show the direction of the electric field between the plates.
b. In terms of V and fundamental constants, determine the speed of the electron when it
leaves the electric field.
c. Describe the electron path in the magnetic field.
d. In terms of V, B and fundamental constants determine the radius of the circle that the
electron describes in the magnetic field.
e. If the magnetic field remains unchanged, what could be done to cause the electron to follow
a straight path in the magnetic field?
2. A positively charged particle with a mass m and charge q is accelerated through a potential
difference V between two vertical plates. The particle then passes into a region of uniform
magnetic field B, directed out of page.
a. Find the potential difference V necessary to give the particle a speed v as it leaves the
electric field.
b. On the diagram above, sketch the path of the particle in the magnetic field.
c. In terms of mass m, charge q, speed v, and magnetic field B, find the radius r of the circular
path of the particle.
d. An electric field E is establish in the same region as the magnetic field. The electric field
causes the particle to pass the region of two fields undeflected.
i.
Show the direction of E on the diagram above.
ii.
Determine the magnitude of E.
3. An electron is emitted from a cathode in a cathode ray tube and is accelerated by an electric
potential difference Ɛ. The electron passes into a region of uniform magnetic field B, directed
out of the page. The mass of the electron is m and the charge is e.
a. Find the potential difference Ɛ necessary to give the electron speed v as it enters the
magnetic field.
b. On the diagram above sketch the path of the electron in the magnetic field.
c. Develop the expression for the radius of the circular path of the electron in the magnetic
field.
d. An electric field E is now established in the same region as the magnetic field, so that the
electron passes through the region undeflected.
i.
Determine the magnitude of E.
ii.
Find the direction of E on the diagram above.
4. The diagram above shows a cross section of a cathode ray tube. An electron in the tube is
accelerated by an electric field established between cathode and anode. The speed of the
electron is 1.9×107 m/s. When the electron passes a region with a uniform magnetic field of
strength 5×10-4 T it becomes deflected upward.
a. Indicate the direction of the magnetic field.
b. Find the magnitude of the magnetic force acting on the electron.
c. Find the radius of the curvature that the electron describes in the magnetic field.
An electric field is established in the region of the magnetic field which makes the electron’s
path undeflected.
d. Find the magnitude of the electric field.
e. Indicate the direction of the electric field.
5. A charged particle of mass m and charge q is accelerated from rest by a uniform electric field
with a potential difference Ɛ established between two parallel plates. The particle enters a
uniform magnetic field of magnitude B oriented perpendicular to the plane of the page. The
path of the particle is curved in a semicircle by the magnetic force.
a. What is the charge on the particle?
b. What is the direction of the magnetic field?
c. What is the speed of the particle when it enters the magnetic field?
d. Find the magnetic force of the particle.
e. Find the radius of the curvature of the particle’s path in the magnetic field.
f. How much worked done by the magnetic field of the particle?
6. In the mass spectrometer, particles with charge q are accelerate from rest through a potential
difference in Region I. I region II containing both fields magnetic B and electric E, they move in a
straight line. Finally, when particles enter Region III containing only a magnetic field B they move
in a circular path of radius R before striking the detector.
a. In the diagram above, indicate the direction of the electric field in Region II.
b. Determine the speed v of the particles as the enter Region III.
c. Determine the mass of the charged particles.
d. Determine the acceleration potential difference Ɛ in Region I.
e. Determine the acceleration of the particles in Region III.
f. Determine the time that it takes the particles to complete the semicircular path In region III.
7. A group of students, working in the physics lab, built an “Electromagnetic Vertical Launcher”.
The apparatus includes an electric circuit with a 120 V battery, connected in series to a 100 Ω
resistor, switch, and thin 500 g metallic rod that is placed on two horizontal conducting
supports. The rod has a length of 40 cm and is placed in a uniform horizontal 1.5 T strong
magnetic field.
a. On the diagram below show all the applied forces on the rod when the switch is closed.
b. Find the normal force in each support when the switch is closed.
c. What is the minimum voltage has to be applied in order to keep the rod weightless?
d. The resistor is replaced with much smaller value of 5 Ω resistor. When the switch is closed
find the instantaneous acceleration of the rod.
e. If the rod moves 10 cm inside the magnetic field, what is the velocity of the rod as it leaves
the field?
f. What is the maximum height reached by the rod from its original position?
8. A conducting rod with mass m and length L moves on the top of two horizontal rails that are
connected to a battery. The battery maintains a constant current in the circuit. Assuming
friction, air resistance, and electrical resistance are negligible answer the following:
a. Find the direction and magnitude of the net force on the rod.
b. Determine the speed of the rod as a function of time.
c. Find the distance d that the rod must move from rest to reach speed v.
d. If the coefficient of friction is µ, find the new distance that the rod must move in order to
attain the same speed v found in part (c).