# Charge In B-Field

The EJS Charge In B-Field model allows the user to simulate moving charged particles in two identical uniform magnetic fields separated by a zero magnetic field gap. A charge moving in a magnetic field experiences a magnetic force given by the Lorenz force law

where theta specifies the angle between the velocity vector and the magnetic field. In this simulation, the velocity and B-field are perpendicular (theta = 90 degrees) and the force is maximum. You can adjust the magnitude of the magnetic field B, the mass m and charge q of the charged particles. The slider d controls the width of the field free region (it is a percentage of half the window width).

1. When B is positive, which way do positively charged particles circle (clockwise or counter-clockwise). Use the right-hand rule to determine if the field points into or out of the screen?
2. Explain why particles traveling in the white (field free) region, travel in a straight path. Charged particles that remain in the green region (uniform magnetic field) experience uniform circle motion. Why? What provides the centripetal force?
3. Since all the particles have the same mass, same charge and experience the same force, what accounts for particles moving in circles of different radii (for the ones that stay in the uniform magnetic field)? How can you change the different parameters to decrease the radius? Explain why each change results in a smaller radius.
4. Optional: If you have EJS installed, modify this model to simulate a cyclotron. It may be useful for you to know that you can change the number of particles n from Model -> Variables -> charged particle vars (tab). It may also be helpful to look on the Model ->Initialization page to see how the initial position and velocity of the particle(s) is(are) set as well as looking at the Model-> Custom page to see the equations of motion for a particle in the magnetic field as well as the gap region.

## References:

The Lorenz force law is described in most introductory physics and electromagnetism terxtbooks.

- Douglas Giancoli, Physics: Principles with Applications sixth edition, pages 560-563.
- David Griffiths, Introduction to Electrodynamics, third edition, p 202-214.

### Credits:

The Charge In B-Field Model was created by Fu-Kwun Hwang using the Easy Java Simulations (EJS) modeling tool. It was adapted to EJS version 4.1 by Robert Mohr and Wolfgang Christian at Davidson College. Additional exercises were added by Anne J Cox. You can examine and modify the model for this simulation if you have Ejs installed by right-clicking within the simulation and selecting "Open Ejs Model" from the pop-up menu.

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.