Helmholtz Composition

Finding the Charge to Mass Ratio from the Electron With a

Uniform Magnet Field Produced by Helmholtz Coils

Summary

The impose to mass ratio with the electron was found to get [pic] having a percent big difference from the acknowledged value ([pic]) of 1. 1% when tweaked for the Earth's magnet field. Devoid of taking the Earth's magnetic discipline into consideration, the charge to mass rate was identified to be [pic] with a percent difference of 5. 3%.

STUDENT:

PARTNER:

INSTRUCTOR:

DATE:

MOORPARK COLLEGE OR UNIVERSITY

THEORY

We all seek the magnetic discipline along the axis of the two Helmholtz coils in number 1 .

[pic]

Figure you

First, thinking about the magnetic discipline due to the coils on the left, the magnetic discipline, B, along the normal axis of a coils is defined as,

[pic](1)

Where And is the volume of loops inside the coil.

By simply definition, the magnetic dipole moment may be expressed because,

[pic](2)

Furthermore, substituting (2) into (1) yields,

[pic]

By extrapolating this consequence, the magnet field because of the coil on the right can be,

[pic]

[pic]

Since the current in the two coils movement in the same direction, then a net magnetic field is definitely the sum from the two matching magnetic areas.

[pic](3)

For the point half way between the shelves,

[pic]

therefore ,

[pic]

[pic](4)

Next, replacing for the magnetic dipole moment in equation (2),

[pic]

[pic](5)

The pressure on an electron within this permanent magnet field is usually,

[pic](6)

wherever e is definitely the charge on an electron, sixth is v is the speed, and r is the radius of the electron path. Resolving for velocity in (6),

[pic](7)

In addition , potential energy can be related to potential difference as follows,

[pic](8)

where V is the potential difference.

Following, substituting (7) into (8),

[pic]

[pic](9)

Finally, substituting (5) in (9) uncovers our doing work equation,

[pic]

[pic](10)

PURPOSE OF THE EXPERIMENT

This lab will experimentally determine the charge to mass proportion of an electron.

PROCEEDURE

Line the e/m apparatus because shown in figure 2 .

[pic]

Physique 2

The evacuated step, which houses the electron beam, will probably be centered between the two Helmholtz coils. Numerous voltages happen to be applied to the electron gun, along with assorted currents supplied across the Helmholtz coils. Record the inner and outer radius of the electron beam arc that appears in the cleared out chamber.

THE DATA

Four voltages were put on the electron gun, that were 150V, 200V, 250V, and 300V. Four currents were then applied to the Helmholtz coils for each voltage setting. The inner and outer radius was considered for each current applied.

Table 1, at the back of this record, shows your data collected.

In addition , the radius, and separating, of the two Helmholtz coils was 15cm and each coil had 145 loops.

EXAMINATION

The electron charge to mass ratio can be found employing equation (10). Table you shows the ratio worked out using the inner and outer electron beam radius.

Table one particular shows that the e/m rate for the lining radius can be,

[pic](11)

and for the outer radius is,

[pic](12)

Since the recognized value of e/m can be,

[pic]

the percent big difference from result (11) plus the accepted value is,

[pic]

and the percent difference coming from result (12) is,

[pic]

Since the end result obtained making use of the outer radius is closer to the recognized value, this can be the result that may be preferred.

COMPENSATING FOR EARTH'S MAGNETIC DISCIPLINE

The Earth's magnetic field strength in Moorpark College or university is,

[pic](13)

Table 2, attached to your back section of this lab record, shows the magnetic field due to the two...



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