IB Physics HLTopic 4 — Force FieldsPaper 1 & 2Line density = field strength~16 min read
Mapping Electric Fields
A field has a strength and a direction at every single point in space. You cannot write that down. But you can draw it — and the drawing carries both pieces of information at once. The direction of a line tells you where a positive charge would be pushed. The spacing of the lines tells you how hard. Crowded lines mean a strong field. That is the entire code, and once you can read it you can read any field diagram in the book.
📘 What you need to know
Field lines show the direction and the magnitude of an electric field
Lines are always directed from positive to negative — the way a positive test charge would move
Field is stronger where lines are closer together, weaker where they are further apart
Around a point charge the field is radial: outwards from +, inwards to −. It is non-uniform
Between parallel plates the field is uniform: lines are parallel and equally spaced
Field lines are always perpendicular to the surface of a conductor, and to the surface of a point charge
Inside a charged conducting sphere the field is zero. The charge sits on the surface
Between two like charges there is a neutral point where the resultant field is zero, and the lines do not connect
Field lines never cross, must touch the surface of the charge or plate, and must always have labelled arrows
Reading the code
Two rules, and everything else follows from them.
Direction. The arrow shows the force on a small positive test charge. So lines point away from positive charges and towards negative ones.
Density. The spacing represents the field strength. Lines packed close together mean a strong field; lines spread wide apart mean a weak one.
That second rule is the one worth money. A question will show you a diagram and ask “at which point is the field strongest?” — and the answer is never in a calculation. It is wherever the lines are most crowded. Learn to answer that question with your eyes.
Line density and the size of the charge
Around a point charge, the lines all start on the charge’s surface, equally spaced, and then spread out as they travel. So a bigger charge does not push its lines further apart — it simply has more of them.
Sphere A has the lowest line density, so the weakest field and the smallest charge. Sphere C has the highest density, the strongest field, and the greatest charge.
Notice the two separate facts hiding in that picture:
At the surface of a point charge, the lines are equally spaced — because they must leave perpendicular to it
Further out, the gaps between them grow. Same number of lines, more space to share. That is exactly why E falls with distance
So a radial field is a non-uniform field — the strength changes from place to place. A uniform field is one where the lines are parallel and never converge. Those are the only two kinds you need at HL, and every diagram in this topic is one, the other, or a mixture of both.
Two charges together
Put two charges near one another and the lines from each one distort the other’s. The result depends entirely on the signs.
Every line here was computed by following the field, not sketched by eye. Note that no line ever crosses another — if two crossed, the field would have two directions at one point, which is nonsense.
Opposite charges
Lines run from the positive charge to the negative charge
They connect the two surfaces, and that connection represents the attraction
Bring the charges closer and the lines between them crowd together — a stronger attractive force
Like charges
Lines point away from two positives (or towards two negatives)
They do not connect. The gap of empty space between them represents the repulsion
At the midpoint there is a neutral point: the two fields are equal and opposite, so the resultant field is zero
The neutral point sits at the midpoint only when the two charges are equal. Make one of them bigger and the neutral point slides towards the smaller charge — it has to, because you must get closer to a weak charge for its field to match a strong one. If a question shows an off-centre neutral point, it is telling you which charge is larger.
Charged conducting spheres
Charge a metal sphere and the excess charges, all the same sign, repel each other until they are as far apart as they can get. That means evenly spread over the surface. None ends up inside.
The field outside is identical to that of a point charge sitting at the centre — which is why you may use E = kQ/r2 for a sphere at all.
Why the lines must be perpendicular
This is a lovely little argument, and it is worth marks. Suppose a field line met the surface at some slanting angle. Then it would have a component parallel to the surface.
Field lines show the direction of the force on a charge
A parallel component would push the surface charges sideways
They are free to move, so they would move — and they would keep moving
Repulsion rearranges them until the parallel component is zero
Which leaves the field lines perpendicular to the surface. Nothing else is stable
The same reasoning kills the field inside. Wherever you stand within the conductor, the surface charges surround you, and every pull is exactly balanced by a pull the other way. The forces cancel, and E = 0.
Uniform fields and line density
Between parallel plates the lines run straight from the positive plate to the negative plate, parallel and equally spaced. Equally spaced means the same strength at every point, and a test charge feels the same force wherever you put it.
Raise the potential difference and you do not spread the lines out — you pack more of them into the same gap. Higher density, stronger field, greater force on a test charge.
A point charge near a plate
Put a charged sphere in front of an oppositely charged plate and the field is a blend of the two pictures. Near the sphere the lines are radial. As they approach the plate they straighten out, and they meet it perpendicularly — because it is a conductor, and the argument above still applies.
✏️ Drawing field lines that score
Put arrows on every line. Every one. Unlabelled lines score nothing.
Arrows run + to −: out of positive charges, into negative charges and plates.
Touch the surfaces. Lines must start and end on the charge or plate, not near it.
Meet conductors at 90°. Spheres, plates, everything.
Never let two lines cross. The field cannot point two ways at once.
Uniform field? Straight, parallel, equally spaced. Radial? Equally spaced at the surface, spreading out beyond.
Arrow direction
tells you
where a + charge would go
and the spacing
tells you the strength
WE 1
Sketch the electric field lines between a positive point charge and a negative point charge of equal magnitude. State three rules you have followed.
Step 1 — get the directions right
Lines point radially outwards from the positive charge.
Lines point radially inwards to the negative charge.
Every arrow therefore runs from + to −.
Step 2 — connect the surfaces
Because the charges are opposite, the lines leave the + and land on the −.
They must touch both surfaces.
Step 3 — the three rules to statearrows on every line, drawn + to −lines meet each surface at 90°lines never crossThe lines are most crowded in the gap between the charges, which is exactly where the field is strongest. Draw more lines through the middle than round the back and the examiner will see that you understand density.
WE 2
Two identical positive charges are held a fixed distance apart. (a) Describe the field lines midway between them. (b) Explain what happens to the neutral point if one charge is made larger. (c) A student draws two field lines crossing. Explain why this must be wrong.
(a) midway between two equal positive charges
Each charge produces a field of the same magnitude there.
They point in opposite directions, so they cancel.
a neutral point — no field lines pass through it(b) make one charge larger
To balance a stronger field you must be closer to the weaker charge.
the neutral point moves towards the smaller charge(c) why lines cannot cross
A field line shows the direction of the field at each point.
At a crossing the field would have two directions at once.
impossible — the field has one unique direction everywhereIn (a) note the careful phrasing: the field is zero at the neutral point, but the potential is not. Those are different quantities, and a later page will make a great deal of that difference.
WE 3
(a) Explain why the field lines leaving a charged conducting sphere are always perpendicular to its surface. (b) Two isolated spheres X and Y have the same radius. Sphere X has 8 field lines drawn around it, sphere Y has 24. Compare the charge on each, and the field strength at their surfaces.
(a) the perpendicular argument
Suppose a line met the surface at an angle.
It would have a component of force parallel to the surface.
Surface charges are free to move, so they would move.
They rearrange until the parallel component is zero.
so the field must be perpendicular to the surface(b) reading the line density
Line density is proportional to charge.
24 / 8 = 3Y carries three times the charge of X
Same radius, so at the surface E = kQ/r² with the same r.
the field at Y’s surface is three times that at X’sPart (b) only works because the radii are equal. Change the radius too and you must go back to E = kQ/r² properly — line counting compares charge, not field strength, unless the geometry matches.
💡 Top tips
Label every arrow. It is the single most commonly dropped mark in this topic.
Lines must touch the surface of the charge or plate — not stop short of it.
Meet a conductor at 90°. Always. Spheres and plates alike.
Never cross two lines. The field has one direction at each point.
“Where is the field strongest?” → where the lines are closest together.
Radial field = non-uniform. Uniform field = parallel, equally spaced lines.
A neutral point lies at the midpoint only for equal charges, and shifts towards the smaller one otherwise.
⚠ Common mistakes
Drawing field lines with no arrows, or with arrows running − to +
Letting lines cross, or stop in mid-air instead of on a surface
Drawing lines that meet a conductor at a slant instead of at 90°
Connecting the lines between two like charges. They repel — the lines stay apart
Saying the field is strong “because there are lots of lines”. It is the spacing that matters, not the count
Drawing field lines inside a charged conductor. The field there is zero
Assuming the neutral point is always at the midpoint. Only if the charges are equal
Confusing a field line with the path a charge would take. It only gives the direction of the force
Quick recap: Field lines carry two pieces of information. Their direction is the force on a small positive test charge, so they run + to −. Their spacing is the field strength: close together means strong. Around a point charge the field is radial and non-uniform; between parallel plates it is uniform, with parallel, equally spaced lines. Lines meet conductors at 90°, and never cross. Inside a charged conducting sphere, E = 0. Between two like charges sits a neutral point, and their lines never connect.
There is a quantity hiding in all of this that we have carefully not named. Pushing a positive charge against the arrows costs you energy — and the closer you shove it to a positive charge, the more it costs. That stored energy per unit charge has a name, it is a scalar (no arrows to worry about, no vector addition), and it is often far easier to work with than the field itself. Next page: Electric Potential.
Field line diagrams costing you marks?
Book a free meeting and we’ll practise sketching dipoles, neutral points and conductor surfaces until the arrows go on automatically.
