# ElectricField and MagneticField

> ElectricField is manim-physics' ElectricField: an arrow on every grid point of x_range by y_range, pointing along the field of charges and coloured by…

Page: https://fframes-kit.pages.dev/docs/physics/electric-field-and-magnetic-field/
Cargo feature: `physics` (`fframes-kit = { version = "..", features = ["physics"] }`)

`ElectricField` is manim-physics' `ElectricField`: an arrow on every grid point of
`x_range` by `y_range`, pointing along the field of `charges` and coloured by its strength
(`colors` from `min_magnitude` to `max_magnitude`), with each charge as a glowing
`ChargeGlow`. `lines_per_charge` adds the field lines of `Field`. `charges` is a plain prop:
compute it from `ui.seconds()` and the arrows and lines follow, the lines traced again each
frame. `ChargeGlow { charge, .. }` draws one charge on its own. Gallery scenes:
`ElectricField`, `ChargeGlow`.

Gallery clip of `ElectricField`: https://fframes-kit.pages.dev/media/scenes/ElectricField-6a1a8339.mp4

Gallery clip of `ChargeGlow`: https://fframes-kit.pages.dev/media/scenes/ChargeGlow-356589e6.mp4

The glow follows the charge's position in `ui.space`. Its disc radius is `radius` pixels
times the square root of the absolute charge, clamped to half through twice `radius`.
The sign and colour distinguish positive from negative charges.

```rust
use fframes_kit::prelude::*;

fn charge<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    let y = 0.7 * f64::from(ui.seconds()).sin();
    ui.show(ChargeGlow {
        charge: Charge::new(0.0, y, -4.0),
        radius: 75.0,
        ..ui.defaults()
    })
}
```

`MagneticField` is the field of `wires` in the page, by the Biot–Savart law (`μ₀` left out).
A `Wire::Through { x, y, current }` crosses the page (current out of it when positive) and
circles its field around it; a `Wire::Segment { from, to, current }` lies in the page, and
its field there points out of or into the page. Where the field lies mostly in the page the
grid shows an arrow, otherwise a ⊙ (out) or ⊗ (in) sized by its strength.
`magnetic_field(&wires, x, y)` returns `(B_x, B_y, B_z)`. Gallery scene: `MagneticField`.

Gallery clip of `MagneticField`: https://fframes-kit.pages.dev/media/scenes/MagneticField-84d64eef.mp4

```rust
use fframes_kit::prelude::*;

fn fields<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    // a negative charge circling a positive one
    let angle = 0.6 * f64::from(ui.seconds());
    let electric = ui.show(ElectricField {
        charges: vec![
            Charge::new(-1.0, 0.0, 2.0),
            Charge::new(-1.0 + 3.0 * angle.cos(), 2.0 * angle.sin(), -1.0),
        ],
        lines_per_charge: 8,
        ..ui.defaults()
    });
    let magnetic = ui.show(MagneticField {
        wires: vec![
            Wire::Through { x: -2.0, y: 0.0, current: 1.0 },
            Wire::Segment { from: (1.0, -1.0), to: (4.0, -1.0), current: 2.0 },
        ],
        ..ui.defaults()
    });
    svgr!(<g>{electric}{magnetic}</g>)
}
```

## API

Components are plain structs. Set the fields you need and fill the rest with `..ui.defaults()`: the defaults below come from the current theme (`theme.` values are fields of `Theme`).

### ElectricField

Manim-physics' `ElectricField`: an arrow at every grid point of `x_range` by `y_range` (units of `ui.space`) along the field of `charges`, `length(|E|)` units long and coloured by `|E|` from `colors[0]` at `min_magnitude` to the last colour at `max_magnitude`, like [`ArrowVectorField`](https://fframes-kit.pages.dev/docs/layout-and-shapes/coordinate-systems.md). Grid points closer than `clearance` units to a charge get no arrow. With `lines_per_charge` above 0 the field lines of `Field` are drawn too, and with `show_charges` every charge as a `ChargeGlow`.

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `charges` | `Vec<Charge>` | `Vec::new()` | The charges that make the field; each has a position in units of `ui.space` and a signed strength. |
| `x_range` | `Range` | `Range::new(-7.0, 7.0, 0.5)` | Grid columns of the arrows: `x` from min to max in steps, in units of `ui.space`; the field lines run half a unit beyond. |
| `y_range` | `Range` | `Range::new(-4.0, 4.0, 0.5)` | Grid rows of the arrows: `y` from min to max in steps, in units of `ui.space`; the field lines run half a unit beyond. |
| `arrows` | `bool` | `true` | Draws the arrow at every grid point. |
| `length` | `fn(f64) -> f64` | `sigmoid_length` | Length in units of `ui.space` of an arrow for a field of magnitude `\|E\|`. |
| `colors` | `Vec<Color>` | `vec![theme.colors.muted, theme.colors.accent, theme.colors.highlight]` | Colour ramp of the arrows: the first colour at `min_magnitude`, the last at `max_magnitude`. |
| `min_magnitude` | `f64` | `0.0` | Field magnitude that gets the first colour of `colors`. |
| `max_magnitude` | `f64` | `2.0` | Field magnitude that gets the last colour of `colors`. |
| `clearance` | `f64` | `0.3` | Grid points closer than this to a charge, in units of `ui.space`, get no arrow. |
| `lines_per_charge` | `usize` | `0` | Field lines traced out of each charge; 0 draws none. |
| `line_color` | `Color` | `theme.colors.muted` | Colour of the field lines. |
| `show_charges` | `bool` | `true` | Draws every charge as a `ChargeGlow`. |
| `glow` | `bool` | `true` | Gives the charges a soft glow. |
| `charge_radius` | `f32` | `26.0` | Charge disc radius in pixels for a charge of 1. |
| `positive_color` | `Color` | `theme.colors.highlight` | Colour of positive charges. |
| `negative_color` | `Color` | `theme.colors.accent` | Colour of negative charges. |
| `stroke_width` | `f32` | `theme.stroke.thin` | Width of the arrows and the field lines in pixels. |
| `enter` | `Option<FadeIn>` | `None` | Fade in at the start; `None` for none. |
| `exit` | `Option<FadeOut>` | `None` | Fade out before the end; `None` for none. |

Methods:

- `fn at(&self, x: f64, y: f64) -> (f64, f64)`: The field at `(x, y)`: the sum of `q r̂ / r²` over `charges`.

Feature `physics` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/physics/electro.rs#L168)

### ChargeGlow

Manim-physics' `Charge` drawn: a disc at the charge with its sign, `radius` pixels for a charge of 1 and growing with the square root of `|q|` (half to twice that), in a soft glow with `glow`. Positive charges are `positive_color`, negative ones `negative_color`. The data is a `Charge`, which `Field` and `ElectricField` take as well.

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `charge` | `Charge` | `Charge::new(0.0, 0.0, 1.0)` | The charge to draw: position in units of `ui.space` and its signed strength `q`. |
| `radius` | `f32` | `26.0` | Disc radius in pixels for a charge of 1; it grows with the square root of `\|q\|`. |
| `glow` | `bool` | `true` | Draws a soft glow of rings around the disc. |
| `positive_color` | `Color` | `theme.colors.highlight` | Colour of a positive charge. |
| `negative_color` | `Color` | `theme.colors.accent` | Colour of a negative charge. |
| `sign_color` | `Color` | `theme.colors.background` | Colour of the `+` or `−` sign on the disc. |
| `enter` | `Option<FadeIn>` | `None` | Fade in at the start; `None` for none. |
| `exit` | `Option<FadeOut>` | `None` | Fade out before the end; `None` for none. |

Methods:

- `fn disc_radius(&self) -> f32`: The disc's radius in pixels.

Feature `physics` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/physics/electro.rs#L26)

### MagneticField

Manim-physics' `MagneticField` in the page: on every grid point of `x_range` by `y_range` (units of `ui.space`) the field of `wires`. Where it lies mostly in the page it is an arrow `length(|B|)` units long, otherwise a circle `length(|B|)` units across with a dot (out of the page) or a cross (into it). Both are coloured by `|B|` from `colors[0]` at `min_magnitude` to the last colour at `max_magnitude`. Grid points closer than `clearance` units to a wire are left out. With `show_wires` a wire through the page is a disc with a dot or a cross, a segment is a thick line with an arrow along its current. `wires` is a plain prop, so the field follows wires computed from `ui.seconds()`. Everything fades with `enter` and `exit`.

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `wires` | `Vec<Wire>` | `Vec::new()` | The wires that make the field: a long wire through the page or a segment in it, each with a current. |
| `x_range` | `Range` | `Range::new(-7.0, 7.0, 0.5)` | Grid columns: `x` from min to max in steps, in units of `ui.space`. |
| `y_range` | `Range` | `Range::new(-4.0, 4.0, 0.5)` | Grid rows: `y` from min to max in steps, in units of `ui.space`. |
| `length` | `fn(f64) -> f64` | `sigmoid_length` | Size in units of `ui.space` of an arrow, or of the circle for a field out of or into the page, for a field of magnitude `\|B\|`. |
| `colors` | `Vec<Color>` | `vec![theme.colors.muted, theme.colors.accent, theme.colors.highlight]` | Colour ramp: the first colour at `min_magnitude`, the last at `max_magnitude`. |
| `min_magnitude` | `f64` | `0.0` | Field magnitude that gets the first colour of `colors`. |
| `max_magnitude` | `f64` | `0.5` | Field magnitude that gets the last colour of `colors`. |
| `clearance` | `f64` | `0.3` | Grid points closer than this to a wire, in units of `ui.space`, get no mark. |
| `show_wires` | `bool` | `true` | Draws the wires: a disc with a dot or a cross for a wire through the page, a thick line with an arrow for a segment. |
| `wire_color` | `Color` | `theme.colors.title` | Colour of the wires. |
| `wire_radius` | `f32` | `22.0` | Radius in pixels of the disc of a wire through the page. |
| `stroke_width` | `f32` | `theme.stroke.thin` | Width of the arrows and rings in pixels; wires are drawn three times as thick. |
| `enter` | `Option<FadeIn>` | `None` | Fade in at the start; `None` for none. |
| `exit` | `Option<FadeOut>` | `None` | Fade out before the end; `None` for none. |

Methods:

- `fn at(&self, x: f64, y: f64) -> (f64, f64, f64)`: The field at `(x, y)`, see `magnetic_field`.

Feature `physics` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/physics/magneto.rs#L89)