Finding velocity of particles in a uniform magnetic field

Click For Summary
SUMMARY

The discussion focuses on calculating the velocity of charged particles moving in a uniform magnetic field of 10 T and an electric field of 30,000 V/m. The trajectory of the particles is linear within the capacitor and circular outside, with a radius of 1 cm. The derived velocity of the particles is 3000 m/s, determined using the equation r = mv/qB, where the mass of the particles is not specified. The analysis emphasizes the forces acting on the particles, particularly the magnetic force and the electric force, while maintaining a constant speed between the capacitor plates.

PREREQUISITES
  • Understanding of Lorentz force and its components in electric and magnetic fields.
  • Familiarity with the right-hand rule (RHR) for determining the direction of magnetic forces.
  • Knowledge of the relationship between radius, mass, charge, and magnetic field strength in circular motion.
  • Basic principles of electric fields and their effects on charged particles.
NEXT STEPS
  • Study the derivation of the equation r = mv/qB for charged particles in magnetic fields.
  • Explore the concept of electric field strength and its impact on particle motion.
  • Learn about the forces acting on charged particles in combined electric and magnetic fields.
  • Investigate the applications of charged particle motion in devices like cyclotrons and mass spectrometers.
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in the dynamics of charged particles in electric and magnetic fields.

ILstudent122
Messages
1
Reaction score
0

Homework Statement


Given are a uniform electric field, E = 30,000 V/m inside a capacitor (see picture), and a uniform magnetic filed, B = 10 T, perpendicular to the plane of the page, present in all of the area.

Identical charged particles are moving in a trajectory marked by the dashed line, under the influence of the two fields: The trajectory inside the capacitor is a straight line, and the trajectory outside the capacitor is circular, with radius r = 1 cm.

fig10.gif


What is the velocity v of the charged particles?

Homework Equations



Possibly r = mv / qB , but I don't know the mass of the particle.
Maybe E = F/q

The Attempt at a Solution



I know that the magnetic field is into the page based on the RHR. The particle is in circular motion because of the velocity and magnetic force vectors. The answer is v = 3000 m/s but I have no idea how it was derived.
 
Physics news on Phys.org
How many forces act on the particles while they are between the plates of the capacitor?

What can you say about these forces given the fact that the particles are traveling in a straight line with a constant speed between the plates?
 
Just noticed that this is your first post at PhysicsForums, ILstudent122. Welcome!
 
Last edited:

Similar threads

A Charged Particle moving in Uniform Magnetic Field
  • · Replies 2 ·
Replies
2
Views
2K
Magnetization of a paramagnetic sphere
  • · Replies 11 ·
Replies
11
Views
2K
Circular trajectory traveled by a charged particle in a magnetic field
  • · Replies 3 ·
Replies
3
Views
2K
A particle's momentum in a magnetic field
  • · Replies 3 ·
Replies
3
Views
1K
Spring-mediated dipole in a magnetic field
  • · Replies 31 ·
2
Replies
31
Views
3K
Question on magnetism: Circular motion of charged particle in a Magnetic Field
  • · Replies 34 ·
2
Replies
34
Views
2K
Finding a Parametric Solution for Particle Trajectory in Magnetic Field
  • · Replies 3 ·
Replies
3
Views
2K
A falling resistive disk in uniform magnetic field
  • · Replies 17 ·
Replies
17
Views
2K
Find the equation of this magnetic field
  • · Replies 6 ·
Replies
6
Views
2K
Ion moving through electric potential difference and magnetic field
  • · Replies 8 ·
Replies
8
Views
2K