Lorentz Coil e/m Calculator

Calculate charge mass ratio from coil beam data. Compare accepted values, uncertainty, and field strength. Export clean reports for careful lab records and review.

Enter Coil and Beam Data

A
V
C/kg
V
A
%

Example Data Table

Turns Coil Radius Spacing Current Voltage Beam Radius Approximate e/m
130 15 cm 15 cm 1.50 A 200 V 4.08 cm 1.76E+11 C/kg
130 15 cm 15 cm 1.83 A 250 V 3.74 cm 1.76E+11 C/kg
130 15 cm 15 cm 2.05 A 300 V 3.66 cm 1.76E+11 C/kg

Formula Used

The calculator first estimates the magnetic field at the center of two circular coils.

B = k μ0 N I R2 / [R2 + (s / 2)2]3/2

Here, k is the correction factor, N is turns per coil, I is current, R is coil radius, and s is coil spacing.

The charge to mass ratio is found from magnetic force and accelerating voltage.

e/m = 2V / (B2 r2)

This comes from qvB = mv2/r and qV = mv2/2.

How to Use This Calculator

  1. Enter the number of turns on each coil.
  2. Enter coil radius and spacing with matching units.
  3. Add the coil current and accelerating voltage.
  4. Measure the circular beam radius and enter it carefully.
  5. Use correction factor one unless your apparatus needs calibration.
  6. Add uncertainty values when you want an uncertainty range.
  7. Press calculate to show results below the header.
  8. Download CSV or PDF for your report.

Understanding Lorentz Coil e/m Results

A Lorentz coil e/m experiment links electricity, magnetism, and circular motion. The calculator turns ordinary lab readings into one clear charge to mass estimate. It is useful for electron beam tubes, Helmholtz coil sets, and classroom verification work.

Why the Measurement Matters

The charge to mass ratio shows how strongly a charged particle responds to electromagnetic fields. For electrons, the accepted value is very large. A small voltage can create high speed motion. A modest coil current can bend the path into a visible circle. Comparing your result with the accepted value helps reveal alignment errors, reading errors, and coil setup issues.

What the Inputs Represent

Voltage is the accelerating potential applied to the beam. Current is the coil current that creates the magnetic field. Coil radius and coil spacing define the field strength near the center. Beam radius is the observed circular path radius. Turns per coil describe how many wire loops strengthen the field. The correction factor lets you model small apparatus differences.

Good Lab Practice

Use consistent units before entering values. Measure the beam radius from the center of the path, not from the tube wall. Read current only after the supply is stable. Keep the beam centered between both coils. Repeat the reading at several voltages and currents. Average consistent trials, but investigate outliers before reporting them.

Interpreting the Output

The magnetic field result explains how strong the Lorentz force was. The calculated e/m value is the main result. Percent error compares the result with the accepted electron value. The uncertainty estimate gives a practical range based on your input tolerances. If percent error is high, check the radius first. Radius enters the formula squared, so a small mistake matters.

Using Exports

CSV export is useful for spreadsheets and lab notebooks. PDF export gives a quick printable record. Include the formula section with your report. Mention all assumptions, especially coil spacing and correction factor. The calculator is an aid, not a replacement for careful observation.

Common Sources of Error

Parallax can shift the beam radius reading. Warm coils can change current slightly. Nearby magnets can disturb the field. Record room conditions, apparatus labels, and repeated trials for better comparison each time.

FAQs

What does e/m mean?

It means charge divided by mass. In this calculator, it usually represents the electron charge to mass ratio, measured in coulombs per kilogram.

Why is beam radius important?

Beam radius appears squared in the formula. A small reading error can strongly change the final e/m value.

What coil spacing should I use?

For a Helmholtz style setup, coil spacing often equals coil radius. Use the actual measured spacing for your apparatus.

What is the correction factor?

It adjusts the field for apparatus calibration, alignment, or known coil differences. Use one when no correction is known.

Why does current affect the result?

Current controls magnetic field strength. A stronger magnetic field bends the beam more for the same speed.

Can I use centimeters?

Yes. Select centimeters for radius or spacing inputs. The calculator converts those values to meters internally.

Why is percent error shown?

Percent error compares your calculated value with the accepted value. It helps judge experiment quality and setup accuracy.

Does uncertainty change the main result?

No. Uncertainty estimates the possible range around the result. It does not alter the central calculated value.

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