Helmholtz Coils Lab Report
Introduction When a charged particle is moving through a magnetic field, it experiences a magnetic Lorentz force given by F ⃗=qv ⃗ ×B ⃗ (1) where q is the charge of the particle, v is the velocity of the charge q and B is the magnetic field. In this experiment, an electron source, which is the heated filament, an electrode and Helmholtz coils are used to generate the magnetic field. Both the electrode and heated filament are placed in a near vacuum container containing a small amount of mercury. …show more content…
The magnetic field produced is given by B= (8µ_0 NI)/(√125 a) (2) where µ_0 is the permeability of free space 4π×〖10〗^(-7)WB/A-m, N is the number of turns 72 for this experiment, I is the current and a is the mean radius of each coil .33 meters. The magnetic field through the Helmholtz coil is shown in Figure 1. The region of this magnetic field that we are concerned with is in the center where the magnetic field lines are nearly uniform. When an electron is accelerated by a potential difference V, it gains kinetic energy equal to the work done on it by the field which is given by 1/2 mv^2=Ve (3) Where V is the anode potential and e is the charge of the electron. The force on an electron traveling perpendicular to a magnetic field is given by F=Bev …show more content…
Since the force is always perpendicular to the electrons direction of motion, it makes it move in a circular path whose plane is perpendicular to the direction of the magnetic field. The force required to keep a body moving in a circle is F=m v^2/r (5)
With radius r and mass m. The required centripetal force is provided by the force exerted on the electron by the negative field m v^2/r=Bev or m v/r=eB
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