C- PHYS102 - LAB 3 - eOver-M-Final

# B for a given velocity as the magnetic field is

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Unformatted text preview: ature r of its orbit. Thus, a fast ­moving particle is harder to deflect by the same magnetic field. [b] For a given velocity, as the magnetic field is increased, r, the radius of the circular orbit gets smaller. The charge of an electron is conventionally denoted by e. Thus for an electron, eq. [2] . can be re ­expressed as: e/m = v/(rB) [3] This is a ratio of two fundamental constants: the electron’s charge and its mass. In the present experiment you will determine this very important ratio e/m by directly observing the orbital radius r of a beam of electrons of speed v moving in a magnetic field of magnitude B. To determine the electron speed v, we note that the electrons in this experiment are generated via thermal emission from a “cathode” (a wire filament) heated to high temperatures. By heating the filament you are providing enough thermal energy to the electrons for them to “evaporate” from the heated filament. Such electrons are then accelerated from nearly zero speed, through an electric potential difference ΔV before entering the region of uniform magnetic field. As an electron moves through the potential difference ΔV, it acquires a kinetic energy equal to: ½mv2 = e ΔV [4] v = [2eΔV /m]1/2 [5] [6] or From eqs.[3] and [5] one can write: e/m = 2ΔV /(rB)2. 2.2 The Helmholtz Coils To create a region of uniform magnetic field B, we will use an arrangement known as Helmholtz coils (Figure 2). It consists of two circular coaxial coils with N turns each separated by a distance equal to the radius of the coils. The two coils have the same number of turns, carry the same current and in the same direction. This arrangement produces an axial Y I I R X O R Figure 2 field that is highly uniform in the region between the coils. The B ­field can be expre...
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## This note was uploaded on 02/01/2014 for the course PHYS 102 taught by Professor N/a during the Spring '08 term at Drexel.

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