Union College
Spring 2015
Physics 121 Lab 7 Introduction
Measuring the Electron’s Charge to Mass Ratio Using Electric and Magnetic Fields
The electron is a fundamental particle of nature and so its charge and mass are two of the input
parameters in the architecture of the universe. A measure of the ratio of these two parameters
enables any other experiment which yields a measure of either one to also provide information of
the other (for example, look up information about the Millikan Oil Drop experiment).
Follow the instructions below for deriving the relevant equations for the lab.
1. In a magnetic field, a moving electron will follow a circular path. Write the equation for the
cyclotron frequency.
(1)
Now, recall that the cyclotron frequency (in radians per second) also equals v/r—substitute this
in for . Note that if the magnetic field and the electron’s velocity are known a measure of the
radius of an electron’s circular path yields a number for the ratio of e/m. Rearrange the equation
to yield an expression for e/m in terms of v, r, and B.
(2)
2. One can give electrons a known velocity by accelerating them across a capacitor gap of
specific V. Consider an electron starting from rest at the negative plate of a capacitor, and
accelerating toward the positive plate. The amount of kinetic energy gained must equal the loss
of potential energy, which is related to the potential difference across the capacitor. Write an
equation that relates the electron’s final velocity to the potential difference of the capacitor:
(3)
3. Substitute in your v from Equation (3) into your Equation (2) to obtain an expression for e/m
of an electron in terms of Vcap, B, and r.
(4)
4. One easy way to get a known and adjustable magnetic field is to use a circular loop of wire,
of radius R and current I. Write the equation for the magnetic field on the axis of a circular loop
of wire of radius R, with current I and N turns, at a distance z from the center of the loop.
What does this equation become if z = R/2 and you have 2 such coils at the same distance?
(5).