Relativity: Initial velocity and e/m of Thomson's experiment

In summary, the experiment uses deflecting plates with an electric field of 1.0×10^4 V/m and a magnetic field of 8×10^-4 T. Without the magnetic field, an angular deflection of 30° is observed. Using the equations u = E/B and e/m = q/m = u/RB, the initial velocity of the electron is calculated to be 1.25×10^7 and the e/m value is 3.125×10^11. However, kinematic equations must be used to accurately calculate q/m from the angular deflection.
  • #1
Matt21
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Homework Statement


In an experiment similar to Thomson’s, we use deflecting plates 5 cm in length with an electric field of 1.0×10^4 V/m. Without the magnetic field, we find an angular deflection of 30°, and with a magnetic field of 8×10^-4 T we find no deflection. What is the initial velocity of the electron and its e/m?

Homework Equations


u = E/B
e/m = q/m = u/RB

The Attempt at a Solution


I'm not sure if I'm using the correct equations but given the equations above, initial velocity is
u = 1.0×10^4/8×10^-4 = 1.25×10^7, and thus e/m is equal to
q/m = 1.25×10^7/(0.05*8×10^-4) = 3.125×10^11
If necessary, can anyone explain what I am doing wrong and perhaps the correct formula to use?
 
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  • #2
Matt21 said:
u = 1.0×10^4/8×10^-4 = 1.25×10^7
OK. Units?

and thus e/m is equal to
q/m = 1.25×10^7/(0.05*8×10^-4) = 3.125×10^11
This is not correct. You will need to use kinematic equations to relate q/m to the angular deflection. Review the kinematics of the Thomson experiment when just the E field is present. It is similar to projectile motion.
 
Last edited:

1. What is relativity and how does it relate to Thomson's experiment?

Relativity is a theory developed by Albert Einstein that explains the relationship between space and time. In Thomson's experiment, relativity is used to calculate the initial velocity and e/m (charge-to-mass ratio) of an electron.

2. How does Thomson's experiment work?

In Thomson's experiment, a beam of electrons is passed through a magnetic field, causing the electrons to deflect. By measuring the deflection angle and the magnetic field strength, the initial velocity and e/m of the electrons can be calculated.

3. Why is the initial velocity of electrons important in Thomson's experiment?

The initial velocity of electrons is important because it affects the amount of deflection in the magnetic field. By knowing the initial velocity, the strength of the magnetic field can be determined, which is necessary for calculating the e/m of the electrons.

4. What is the significance of the e/m of electrons in Thomson's experiment?

The e/m (charge-to-mass ratio) of electrons is a fundamental property of electrons and is important in understanding their behavior in electric and magnetic fields. Thomson's experiment helped to accurately determine this value, which was a major achievement in the field of physics.

5. What implications did Thomson's experiment have on the scientific community?

Thomson's experiment had a significant impact on the scientific community as it provided evidence for the existence of electrons and their properties. It also contributed to the development of the theory of relativity and paved the way for further discoveries in the field of particle physics.

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