University of Wisconsin Green Bay

An electron is traveling to the right with a speed of 8.5 x 106 m/s when a magnetic field is turned on. The strength of the magnetic field is 0.050 T, and it is directed into the paper. Describe the path of the electron after the field has been turned on. (You may ignore relativistic effects.)

  • In this problem, you are asked to relate motion (the path of the electron) to force (magnetic field is directly related to magnetic force, just as g is directly related to gravitational force). Force and motion of a single object are always related through Newton’s Second Law, so this is a force or 2nd Law problem.

  • Step 1:

    In order to determine the direction of magnetic force on an electric charge moving in a i, we need to use the 3-step right hand rule. (Force, velocity and field are all vectors—the 3-step right hand rule relates the direction of these three vectors.)

    Although you now have a free body diagram, you also need to recognize that magnetic force is always perpendicular to the motion of the charge. So when the charge changes direction, the force also changes direction. Continue to step 2 to explore the implications of the changing direction of force on the path of the electron.


    Step 2:

    As the magnetic force acts on the electron, the electron changes direction. Using the right hand rule again shows that force also changes direction. In other words, the magnetic force continues to point perpendicular to velocity and pulls the electron in a clockwise circle.

    To fully describe the path of the electron, you now need to find the size of that circle.

  • The key equation for any problem that relates forces and motion is Newton’s Second Law. Regardless of what quantity you are asked to find, begin with the Second Law. If additional information is needed, it will become apparent as you proceed.

  • The magnetic field causes the electron to move clockwise in a circle with a radius of 9.7 x 10-7 m. Nothing further is needed to describe the path of the electron.

  • In this problem, you are asked to describe the path of a moving charge when you are given information related to the force on that charge. It is a Newton’s 2nd Law problem.

    This is a case where experience helps make the problem easier: any motion of a charge that is perpendicular to a magnetic field gives rise to circular motion of that charge. This is worth noting and remembering for future problems. To describe the path of the charge, then, you merely need to determine the size of the circle and which direction (clockwise or counter-clockwise) the charge moves around it.

    Although you might initially be surprised at how small the circle is, note that the tiny mass of the electron means that you get a huge acceleration for even a small force.