IB Physics SLTopic 4 — Force FieldsPaper 1 & 2Field lines & field maps~7 min read
Mapping Gravitational Fields
You can’t see gravity — but you can draw it. Physicists map a field with field lines: little arrows that show which way a dropped object would be tugged at every point in space. Learn to read and sketch these maps and a planet’s invisible pull becomes a picture you can mark up in the exam.
📘 What you need to know
A gravitational field line (or “line of force”) shows the direction of the force a small test mass would feel there — so it also shows which way that mass would accelerate
For a uniform sphere (a planet, star or moon), you can treat all its mass as a single point at the centre — the field outside looks exactly like a point mass’s
Around a point mass the field is radial: the lines are straight, aimed at the centre, and always point inward — because gravity is attractive only
A radial field is non-uniform: g changes with distance, so the lines are not evenly spaced
Where lines are crowded the field is strong; where they spread apart it’s weak — the spacing is a map of g
Close to a planet’s surface, over a small patch, the lines look parallel and equally spaced: a uniform field, where g is the same everywhere
Golden rule: always draw the arrowheads, pointing toward the centre (radial) or toward the surface (uniform)
First, the Point-Mass Trick
A planet is huge, lumpy and spread out — so how can we possibly talk about one clean “distance r from it”? Here’s the shortcut that makes the whole topic work: if the mass is spread evenly through a sphere, then from the outside its field is identical to that of a single point holding all the mass, sitting right at the centre.
So the Earth, the Sun, the Moon — every tidy ball of matter — can be replaced by an imaginary dot at its middle. That’s why r is always measured from the centre, and why we can draw such neat pictures for something as messy as a real planet.
Same move as pretending all your bag’s weight hangs from its handle — clumsy in reality, but the physics comes out identical and the sums get easy.
What a Field Line Actually Means
Imagine placing a tiny test mass at some point near a planet and asking, “which way does it get pulled?” Draw a little arrow in that direction. Do it everywhere, join the arrows into smooth paths, and you’ve drawn the field. Each line carries two pieces of information at once:
The arrow direction = the direction of the gravitational force on a mass placed there (and so the direction it would start to accelerate).
The spacing of the lines = how strong the field is — crowded lines mean a strong pull, spread-out lines mean a weak one.
test mass in the field
feels an attractive pull
arrow points toward the centre
Because gravity is only ever attractive — it pulls, it never pushes — every gravitational field line points inward, toward the mass making the field. There are no outward arrows in gravity, ever.
The radial field of a point mass: straight lines, all aimed at the centre. Notice the same twelve lines sit close together near the surface and fan apart with distance — that widening is the field getting weaker.
Two Field Shapes You Must Know
Radial fields — the “star-burst” pattern
Around any point mass (or uniform sphere) the lines shoot straight in toward the centre like the spokes of a wheel. This is a non-uniform field: g is different at every distance, which is exactly why the lines aren’t evenly spaced. Step twice as far from the centre and, by the inverse-square law from the field-strength page, g drops to a quarter — you can literally see it as the lines thinning out.
Why the lines fan outg ∝ 1 ÷ r²
Here’s the neat bit: the number of lines is fixed, but as you go outward they’re sharing an ever-bigger sphere of space, so the lines per unit area fall off as 1 ÷ r² — the very same law as g. The spacing isn’t just a rough hint; it tracks the field strength exactly.
lines crowded together
more lines per area
stronger g
lines spread apart
fewer lines per area
weaker g
Uniform fields — the “parallel rain” pattern
Now zoom right in to a small patch just above the ground. The planet’s surface is so vast compared with your patch that its curve flattens out, and those fanning spokes become parallel, equally spaced arrows. That’s a uniform field: same strength, same direction at every point. It’s the everyday gravity you live in — a steady g ≈ 9.8 N kg⁻¹ pointing straight down.
Zoom into a small patch of that radial field and the spokes straighten into parallel rain: a uniform field where g is the same everywhere. It’s a great approximation — over a 100 m building g changes by only about 0.003%.
🎨 How to draw the field in the exam
Decide the shape first — a lone planet or point mass gets a radial star-burst; the ground near a surface gets a uniform set of parallels
For a radial field, aim every line at the centre — straight spokes, evenly spread around the sphere, none of them curved
For a uniform field, rule parallel lines — same spacing, same length, all pointing the same way
Add arrowheads and point them inward — toward the centre, or toward the surface; gravity is attractive, so never draw them outward
Let spacing tell the truth — closer near the surface, wider further out; don’t draw a radial field with evenly spaced lines
Quick recap: field lines point the way a test mass is pulled — always inward. Radial fields (point masses) are non-uniform with lines that fan out; a small patch near a surface is a uniform field with parallel, equally spaced lines. Crowded lines = strong g, spread lines = weak g.
WE 1
A student sketches the gravitational field around a spherical moon. (a) State the direction of the field lines. (b) Explain how the diagram alone tells you that the field strength decreases with distance from the moon.
Part (a) — direction
The lines are radial and point straight inward, toward the centre of the moonbecause gravity is attractive only — a test mass is always pulled toward the mass.Part (b) — reading the spacing
Field strength is shown by how tightly the lines are packed (lines per unit area).
Moving outward, the radial lines fan apart, so fewer pass through each unit of areawider spacing → smaller gSame twelve lines, but sharing a bigger and bigger sphere as r grows — so g falls with distance.
WE 2
Near the Earth’s surface the field is usually drawn as equally spaced, parallel vertical arrows. (a) State what this pattern tells you about the field. (b) Explain why it’s a fair approximation even though the true field is radial.
Part (a) — what the pattern means
Equally spaced + parallel lines mean a uniform fieldsame g in size and direction everywhere≈ 9.8 N kg⁻¹, pointing straight down.Part (b) — why it works
The patch we use is tiny next to Earth’s radius (~6400 km).
Over such a small region the radial spokes are so nearly parallel and evenly spaced that the difference is negligibleso treating the real (radial) field as uniform loses almost nothing near the ground.
💡 Top tips
Arrowheads win marks: a field-line diagram with no arrows, or arrows pointing outward, usually scores zero — gravity is attractive, so they point in
Radial → toward the centre; uniform → toward the surface. Say which type you’re drawing and the direction follows automatically
Spacing is not decoration — it encodes g. Draw radial lines closer near the surface and wider out in space; draw uniform lines perfectly even
Treat spheres as points: a uniform planet or star behaves as if all its mass sits at the centre, which is why the field outside is a clean radial pattern
⚠ Common mistakes
Leaving off the arrowheads, or drawing them pointing away from the mass — gravity never pushes
Drawing a radial field with perfectly even spacing (that’s a uniform field) — radial lines must fan out with distance
Drawing a uniform field with lines that spread or converge — near a surface they stay parallel and equally spaced
Letting field lines cross, or stop in empty space — at any point the pull has one direction, so lines never intersect and always run to the centre
That’s gravity turned into a picture you can read at a glance. Up next: Kepler’s Laws of Planetary Motion — how these same fields set planets sweeping around the Sun, and the tidy link between an orbit’s size and how long a year lasts.
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