# Charged Particle Deflection - CRT, Electric Field Deflection, AC Plates

> Charged particles in electric fields: accelerate with qU₁ = ½mv₀², deflect by y = U₂L²/(4U₁d), find the screen spot, plus CRT sweep, AC plates and practice.

- URL: https://qilingtools.com/en/physics/deflection-tube
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

This tool covers the classic exam model of a charged particle accelerated through U₁ and then sent between deflecting plates. The canvas draws the path, the back-extended exit line and the spot on the screen, and every formula is shown with your numbers substituted. Extra tabs show different ions sharing one path, a CRT oscilloscope sweep, an electron beam between alternating plates and straight-line acceleration, with randomized practice at the end.

## How to use

1. Pick a particle (electron, proton, deuteron, alpha) and set U₁, U₂, plate length L, gap d and screen distance D
2. Press Play to watch it accelerate, bend and hit the screen; read v₀, offset y, tanθ, screen offset Y and the critical voltage
3. Switch to the CRT or AC tab and change the sweep, the signal, the period and the entry time to see the screen picture and exit offsets
4. Try the random problems on the Practice tab and check the worked solution

## Features

- Full accelerate-then-deflect model: parabolic path, exit line through the plate centre, plate hits and critical voltage
- Proton, deuteron and alpha fired together: same path, different speeds, animated at the true speed ratio
- CRT oscilloscope: sawtooth sweep with sine, square or triangle signals, phosphor afterglow, rolling traces and Lissajous figures
- Alternating plates: continuous beam animation, u–t, v_y–t and y–t graphs, fraction hitting the plates
- Straight-line acceleration and braking: gets through or turns back, stopping depth and v–t graph
- Seven kinds of random problems marked with 2% tolerance and step-by-step solutions

## FAQ

### Why does the offset y = U₂L²/(4U₁d) not depend on charge or mass?

Acceleration gives qU₁ = ½mv₀², so mv₀² = 2qU₁. Between the plates y = ½(qU₂/md)(L/v₀)² = qU₂L²/(2mdv₀²). Substituting mv₀² cancels both q and m, leaving y = U₂L²/(4U₁d). Ions of the same sign accelerated from rest by the same voltage and sent through the same plates therefore follow identical paths; they just take different times.

### Why does the exit velocity line pass through the centre of the plates?

At the exit the offset is y = ½at², the vertical velocity is v_y = at and the horizontal distance is L = v₀t. Extending the exit velocity backwards covers a horizontal distance y/tanθ = (½at²)/(at/v₀) = v₀t/2 = L/2. So the particle seems to come straight from the plate centre, and the screen offset is simply Y = (L/2 + D)tanθ.

### How do I know whether the particle hits a plate?

For entry along the centre line it hits when the computed offset exceeds d/2. Setting y = d/2 gives the critical voltage U₂ = 2U₁d²/L². With a larger U₂ the particle lands at x = d√(2U₁/U₂) from the entrance. The tool lists the critical voltage and marks the landing point on the canvas.

### Why does an oscilloscope put a sawtooth on the X plates?

A sawtooth rises linearly, moving the spot across the screen at a steady speed, which turns the horizontal axis into a time axis; then it snaps back and the next sweep starts. The signal on the Y plates moves the spot up and down at the same time, so the screen draws the signal against time. When the sweep period is a whole number of signal periods every sweep lands on the same curve and the picture is stable.

### When do particles leave alternating plates parallel to them?

When the transit time is a whole number of voltage periods. With a square wave each period pushes the particle one way for half a period and brakes it for the other half, so the vertical velocity returns to zero and every particle leaves parallel to the plates. The one entering at t = 0 is displaced most, y = aT²/4 per period; drag the entry-time slider to see the offset change.

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