IB Physics SLTopic 4 — Electric & Magnetic FieldsPaper 1 & 2field lines: + → −~8 min read
Mapping Electric Fields
An electric field is invisible — but we can draw its shape. Field lines turn the numbers from the last page into a picture: which way a charge would be pushed, and where the field is strong or weak. Learn to read and sketch them and you can describe any charge arrangement at a glance.
📘 What you need to know
Field lines show the direction a positive test charge would move: always from + to − (away from positive, towards negative)
The closer the lines, the stronger the field; the further apart, the weaker
Around a point charge the field is radial: lines point out for +, in for −
Between opposite charges the lines connect (+ to −); between like charges they don’t, and there’s a neutral point in the middle where the field is zero
Around a conductor, lines meet the surface at right angles, and the field inside is zero
Between parallel plates the field is uniform: equally spaced parallel lines from the + plate to the − plate
Golden rules: always draw arrows, lines must touch the surface, and they never cross
What Field Lines Show
A field line is the path a tiny positive test charge would follow if released — so the arrow on every line points the way the force acts: away from positive charges, towards negative ones. Two things carry all the information:
Direction — the arrow tells you which way a charge is pushed at that point.
Density — how tightly packed the lines are tells you how strong the field is. Bunched-up lines mean a strong field; spread-out lines mean a weak one.
Around a Single Charge
The simplest picture is a lone point charge. Its field is radial — the lines shoot straight out from (or into) the centre in every direction. For a positive charge they point outwards; for a negative charge they point inwards. Notice the lines are packed tightest right next to the charge, where the field is strongest, and fan apart with distance as the field weakens.
A single charge makes a radial field — lines straight out for + and straight in for −. They’re densest next to the charge (strongest field) and spread out with distance. This looks just like a radial gravitational field, except gravity only ever points inwards, like the negative charge.
Between Two Charges
Put two charges together and the patterns get more interesting — and this is where the difference between attraction and repulsion shows up clearly.
For opposite charges (a dipole), the lines leave the positive charge and curve round to land on the negative one, connecting the two. That linking of the surfaces is the picture of attraction.
For like charges, the lines push away from both charges and never join up. Right in the middle sits a neutral point: a spot where the two fields exactly cancel, so the resultant field there is zero.
Left: a dipole — field lines run from the + charge to the − charge, connecting them (attraction). Right: two like charges — the lines curve away and never meet, with a neutral point in the middle where the fields cancel (E = 0).
Line Density Shows Strength
The spacing of the lines isn’t just decoration — it measures the field strength. Where lines crowd together the field is strong; where they spread out it’s weak. So a charge with a bigger magnitude is drawn with more, denser field lines around it.
Same idea, two sizes: the bigger the charge, the more field lines and the closer together they are — a stronger field. Reading line density is how you compare field strengths straight off a diagram.
The same logic works for a uniform field between parallel plates: the lines are equally spaced, and turning up the voltage packs them closer to make a stronger field. A radial field (around a point charge) is non-uniform — the lines spread with distance, so the field weakens as you move away.
Field Around a Charged Conducting Sphere
A charged conducting sphere spreads its charge evenly over its surface (the like charges repel each other as far apart as they can go). Outside, the field is identical to a point charge at the centre — same radial pattern as before. Two extra rules matter for a conductor:
Field lines always meet the surface at right angles. If they didn’t, there’d be a sideways force pushing charges along the surface until they rearranged and the sideways part vanished.
The field inside the sphere is zero — the forces on a test charge there cancel out completely.
🎨 How to draw electric field lines
Always add arrows — pointing away from + and towards −
Start and end on the charges — lines must touch the surfaces, never float free
Never let lines cross — the field has one direction at each point
Space shows strength — closer lines = stronger field; for a uniform field keep them equally spaced and parallel
Meet conductors at 90°, and remember the field is zero inside a conductor
Quick recap: field lines run + → −, with arrows always shown. Point charges give radial fields (out for +, in for −); opposite charges connect, like charges don’t and leave a neutral point; lines meet conductors at right angles with zero field inside; and closer lines mean a stronger field.
WE 1
Sketch the electric field pattern between a positive and a negative point charge (a dipole). State two rules your sketch must obey.
The pattern
Curved lines running from the + charge to the − charge, connecting their surfaces
Arrows point + → − (away from positive, towards negative)
Lines are closest between the charges, where the field is strongest
Two rules (any two)
• every line has an arrow
• lines start and end on the charges (touch the surfaces)
• lines never crossdipole: + → − connecting lines
WE 2
A metal sphere carries a negative charge. (a) Describe the electric field lines around and inside it. (b) A second sphere is drawn with more closely spaced lines. State what this tells you.
Part (a) — around and inside
Lines are radial, pointing inwards (towards the negative sphere)
They meet the surface at right angles (90°)
Inside the sphere the field is zeroPart (b) — denser lines
Closer lines mean a stronger field, so the second sphere has a
greater magnitude of charge
💡 Top tips
Label every arrow. An unarrowed field line usually loses the mark — the direction is half the information
+ to −, always. Radial out for positive, in for negative; between charges the arrows run from the + charge to the − charge
Density = strength. Comparing two diagrams? The one with lines closer together has the stronger field (and bigger charge)
Conductors: lines hit the surface at 90° and the field inside is zero — a favourite “explain why” question
⚠ Common mistakes
Forgetting the arrows, or drawing them the wrong way (into a + charge instead of out of it)
Letting lines cross, or leaving gaps so they don’t touch the surface of the charge or plate
Connecting the lines between like charges — like charges repel, so their lines don’t join, and there’s a neutral point
Drawing a uniform field with unevenly spaced lines — between parallel plates they must be equally spaced and parallel
That completes the electric side of this topic. Up next: Magnetic Fields — a new kind of field with its own field lines (north to south), made by magnets and by electric currents, plus the right-hand grip rule for the field around a wire.
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