[PDF] e/m Experiment (Magnetron Method)





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Electron Charge to Mass Ratio e/m

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Lab 1: Determination of e/m for the electron

This experiment measures e/m the charge to mass ratio of the electron. This ratio was first measured by J. J. Thomson in 1897. He won a Nobel prize for his 

e/m Experiment (Magnetron Method)

Object:

To determine e/m (Specific Charge) for an electron by magnetron method.

Apparatus Used:

e/m apparatus consisting of power supply fitted with voltmeter and ammeter to read anode

voltage (in volts), anode current (micro amp), solenoid power supply fitted with ammeter to read solenoid current(amp), magnetron valve with base and connecting wires, solenoid fitted with suitable wooden base.

Description:

A magnetron is a thermionic valve with cylindrical coaxial anode and cathode. Electrons emitted

by the cathode travel radially to the anode (see Figure 1), however in the presence of an axial magnetic

field (which can be obtained by placing it inside a solenoid) the path of electrons become curved. At a

critical value of the magnetic field, the path of electrons just touch the anode, any further increase in

magnetic field strength will result in the path of electrons so curved that they do not reach the anode

hence the anode current falls to zero. Measurement of this critical field can be used to determine e/m.

Formula Used :

e/m (Specific Charge) for an electron is given by Where

V= Anode potential

Ra= Anode radius

Bc= magnetic field corresponding to critical solenoid current Ic

Theory:

Magnetron arrangement consists of a cathode in form of a wire fitted at the axis of a cylindrical

anode of radius Ra exists radially. A magnetic field parallel to the axis of cathode (filament) is superposed upon the electric

field by placing the magnetron inside a solenoid such that its axis is coincident with solenoid axis. The

strength of the magnetic field may be varied by controlling the solenoid current Ic .

Let us assume the electrons emit from the cathode with zero initial velocity and begin to

Magnetic Field (B) does not change the speed of an electron however modifies the trajectory of an electron depending on the magnitude of B. Following conditions may arise: (a) B=0 electrons will move radially outwards and strike anode (b) BBc path of electrons will be highly curved and they will not reach anode s. If the anode current (Ia) is studied as a function of solenoid current (IsssIc anode current (Iac point of intersection of tangents (1) & (2) . Tangent (1): drawn at region when anode current is constant Tangent (2): drawn when anode current practically reduces to zero.

Bc can then be calculated as

Where Ic =Critical value of solenoid current for cut-off (in amp)

N= number of turns per meter of the solenoid

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