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Exploring Electron Properties and the Hall Effect: Cathode Rays and Their Applications

This comprehensive overview delves into the properties of electrons, the Hall Effect, and the historical development of cathode rays. It begins with the exploration of cathode ray tubes (CRTs) and their function in the presence of electric and magnetic fields. The discussion includes key experiments, such as those conducted by J.J. Thomson and Millikan, that established important measures of electron behavior. The Hall Effect is examined, illustrating how it generates an electric field in a magnetic field and its practical applications in magnetic field measurement.

mohammad-ramsey
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Exploring Electron Properties and the Hall Effect: Cathode Rays and Their Applications

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  1. Unit 4 Day 4 – Electron Properties & Hall Effect • Cathode Rays and Cathode Ray Tubes • Electron Beam in the Presence on an Electric & magnetic Field • The Velocity Selector • The Hall Effect & Hall EMF

  2. Cathode Rays • In the 1890’s, devices were built called discharge tubes • What was emitted & observed as a “glow” was called cathode rays. It was later determined that these were ionized electrons. Evacuated but back filled with rarified gas

  3. Cathode Ray Tube • Cathode Ray Tube (CRT) starts with a beam of electrons which are passed through a set of parallel plates, and a set of coils, 90° to the plates. • When the E-Field is applied, the electrons curve up. When the B-Field is applied, the electrons curve down.

  4. Electron Properties • Remember, in previous experiments performed by J. J. Thompson, if the Electric and Magnetic forces are balanced: • The electron velocity becomes: • E, B, & r, were all measurable quantities

  5. Electron Properties • Note: In later experiments by Millikan (Oil-drop Experiment), the charge of the electron was established. • Knowing e and e/me, then me was calculated to be:

  6. The Hall Effect • If a current carrying conductor is held fixed in a magnetic field, the magnetic force on the electrons in the conductor is: where vd = drift velocity • The electron will tend to move to the bottom of the conductor (D)

  7. The Hall Effect • The movement of the electron will develop a ΔV between the top (C) and the bottom (D) which will set-up an electric field EH. • This produces an electric force –eEH on the moving electrons (which is upward, equal and opposite to the magnetic force)

  8. The Hall Electric Field & EMF • The EH is called the Hall Field, after E. H. Hall, who discovered this effect in 1879 • The EMF produced by the Hall Field is then: where d is the width of the conductor • The magnitude of the Hall EMF is proportional to the strength of the magnetic field

  9. Hall Effect Applications • A Hall Effect Probe can be constructed to measure the strength of a magnetic field • A Hall Effect device can also be used to measure the drift velocity, given a known magnetic field

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