Lorentz Coil e/m Ratio Experiment Calculator

Calculator Inputs

Accelerating Voltage V

Coil Current I A

Electron Beam Radius r cm

Coil Radius R cm

Number of Turns N

Coil Separation s cm

Accepted e/m Ratio C/kg

Voltage Uncertainty %

Current Uncertainty %

Beam Radius Uncertainty %

Coil Radius Uncertainty %

Separation Uncertainty %

Formula Used

Magnetic field at midpoint:

B = μ₀ N I R² / [R² + (s / 2)²]³ᐟ²

Electron charge to mass ratio:

e/m = 2V / (B²r²)

Percentage error:

Error % = [(measured e/m − accepted e/m) / accepted e/m] × 100

Uncertainty model:

Relative u(e/m) ≈ √[uV² + (2uB)² + (2ur)²]

Here, V is accelerating voltage, I is coil current, N is turns, R is coil radius, s is coil separation, and r is the electron beam radius. All radii are converted to meters before calculation.

How to Use This Calculator

Enter the accelerating voltage from the electron tube supply.
Enter coil current, coil turns, coil radius, and coil separation.
Enter the measured circular beam radius in centimeters.
Add uncertainty percentages if your lab sheet requires them.
Press Calculate to view the result above the form.
Use CSV or PDF export for reports and lab records.

Example Data Table

Voltage V	Current A	Turns	Coil Radius cm	Separation cm	Beam Radius cm	Field mT	e/m C/kg	Error %
200	1.50	130	15.00	15.00	4.00	1.169	1.8296E+11	4.03
250	1.70	130	15.00	15.00	3.65	1.325	2.1384E+11	21.58
180	1.35	130	15.00	15.00	4.45	1.052	1.6426E+11	-6.61

Lorentz Coil e/m Ratio Experiment Guide

The Lorentz coil experiment measures the charge to mass ratio of an electron. It uses a glowing electron beam, an accelerating voltage, and a magnetic field from two circular coils. When the beam enters the field, the Lorentz force bends it into a circle. The observed circle radius gives the needed clue.

Why the Measurement Matters

This experiment links electricity, magnetism, and circular motion. It shows that charged particles follow predictable paths inside magnetic fields. The result can be compared with the accepted electron charge to mass ratio. A close match confirms good alignment, stable current, and careful radius reading.

How the Calculator Helps

Manual calculation can be slow. Small unit mistakes can also change the answer a lot. This calculator converts coil dimensions, estimates the magnetic field, and computes e over m. It also reports percentage error against the accepted value. Optional uncertainty inputs help judge whether the reading is reliable.

Important Inputs

Voltage sets the electron kinetic energy. Coil current sets magnetic field strength. Coil turns and coil radius define how strong the field becomes. Coil separation adjusts the field model. Beam radius is the visible electron path radius inside the tube. These values should be measured carefully.

Good Laboratory Practice

Let the tube warm up before reading the beam. Keep the room dim, so the path is clear. Avoid parallax by viewing the beam straight on. Use steady current and avoid moving nearby magnets. Record several trials, then compare the average. Repeated trials reduce random error.

Interpreting Results

A low percentage error suggests sound data. A high error often points to radius reading problems, wrong units, or unstable current. Coil separation should usually match coil radius for a Helmholtz arrangement. If separation differs, the magnetic field changes. Always record the actual separation used.

Using Exported Reports

The CSV file is useful for spreadsheets. The PDF report is useful for lab submission. Save both with the raw data sheet. This makes later review easier. It also helps teachers verify the method, formula, and assumptions.

Safety Note

Use normal laboratory safety rules. Do not touch powered terminals. Ask an instructor before changing tube wiring, coil connections, or supply ranges during live operation or demonstration sessions.

FAQs

What does this calculator find?

It calculates the electron charge to mass ratio from voltage, coil current, coil dimensions, and beam radius measured in a Lorentz coil experiment.

Which radius should I enter?

Enter the radius of the circular electron beam path. Do not enter the diameter. If you measure diameter, divide it by two first.

Why is coil separation needed?

Coil separation changes the magnetic field at the center. When separation equals coil radius, the setup is close to the Helmholtz condition.

What unit is used for coil radius?

The form accepts coil radius in centimeters. The script converts it to meters before applying the magnetic field formula.

Why does percentage error become large?

Large error can come from wrong beam radius, unstable current, incorrect turns, poor alignment, or using diameter instead of radius.

Can I change the accepted value?

Yes. The accepted ratio field is editable. Keep the standard value unless your instructor gives another reference value.

What does uncertainty mean here?

Uncertainty estimates how input measurement limits affect the final answer. It is a simple independent relative uncertainty model.

Can I use exported files in a report?

Yes. The CSV file supports spreadsheet work. The PDF file gives a compact result summary for lab records.