IB Physics SLTopic 4 — Force FieldsPaper 1 & 2F = EQ~8 min read
Charges in Electric Fields
Swap the magnetic field for an electric one and the story changes shape — literally. A magnetic field bends a charge into a circle; an electric field pushes it in one steady direction and curves it into a parabola, exactly like a ball thrown sideways under gravity. This is the trick behind the old cathode-ray tube and every ink-jet printer.
📘 What you need to know
A charge in an electric field feels a force F = EQ — along the field lines for a positive charge, against them for a negative one
A charge fired across a uniform field (between two charged parallel plates) follows a parabolic path — steady forward speed, plus a steady sideways pull
A positive charge bends toward the negative plate; a negative charge bends toward the positive plate; an uncharged particle sails straight through
The force is the same size and direction everywhere in a uniform field, so the acceleration is constant — this is the projectile analogy
How much it deflects depends on the particle: more charge → more bend; more mass → less bend; more speed → less bend
Contrast with a magnetic field: electric → parabola (constant force), magnetic → circle (force always turning)
What an Electric Field Does to a Charge
Drop a charge into an electric field and it feels a force straight away. The size of that force is beautifully simple — the field strength times the charge:
Force on a charge in an electric fieldF = EQ
Here F is the force (N), E is the field strength (N C−1), and Q is the charge (C). A positive charge is pushed along the field lines; a negative charge is pushed the opposite way. If the charge starts at rest, it simply accelerates in a straight line along the field. The interesting case is when it’s already moving across the field.
Moving Across the Field: the Parabola
Picture a charge shot horizontally into the gap between two charged plates. Its forward speed carries on unchanged, but the field adds a steady sideways force the whole time it’s between the plates. Constant forward motion plus a constant sideways pull is the exact recipe for a parabola — the same maths as a ball rolled off a table, only here “gravity” is the electric force.
Blue lines show the field between the plates. The charge keeps its forward speed but feels a constant downward force (red), so it traces a parabola — bending toward the oppositely charged plate.
Which Way Does It Bend?
The direction is just “opposites attract” applied to the plates. Follow the sign of the charge:
positive charge
→
bends to − plate
negative charge
→
bends to + plate
no charge (neutron)
→
straight through
What Controls the Deflection
Two identical plates, two different particles fired in the same way — they won’t bend by the same amount. Three things decide how sharply a particle turns:
Same plates, same entry, different particles. A big charge bends more; a big mass or a high speed bends less — so a heavy, fast particle barely curves, while a light, slow, highly charged one swings hard toward the plate.
Quick recap: a charge in an electric field feels a constant force F = EQ, so a charge crossing the field traces a parabola (projectile-style). Positive bends to the − plate, negative to the + plate, neutral goes straight. Deflection grows with charge and shrinks with mass and speed.
🎨 Drawing the path in the exam
Charged? If not (a neutron), draw a straight line — no force, no bend
Which plate? Positive charge curves toward the − plate; negative toward the + plate
Shape: start the path horizontal, then let it curve more and more — a parabola, never a circle or a straight diagonal
Compare deflection with q ÷ m (at the same speed): more charge steepens it, more mass or speed flattens it
Match the entry: if two particles enter at the same point and speed, draw both leaving that point together, then separating by their different curvatures
WE 1
A proton is fired horizontally into the uniform field between two parallel plates and follows a curved path toward the negative plate. An alpha particle (charge 2× the proton, mass 4× the proton) is then fired in at the same point with the same speed. Describe how its path compares with the proton’s.
Same direction of bend?
The alpha is also positive → it curves toward the same (negative) plate
Compare the deflection (same E, same v)
deflection ∝ Q ÷ m
alpha ÷ proton = (2 ÷ 4) = 0.5the alpha deflects half as muchTwice the charge would bend it more, but four times the mass wins — so the alpha traces a shallower parabola, curving the same way but only half as far.
WE 2
An electron (charge 1.60 × 10⁻¹⁹ C, mass 9.11 × 10⁻³¹ kg) sits in a uniform electric field of strength 3.0 × 10⁴ N C⁻¹. (a) Calculate the electric force on the electron. (b) Calculate its acceleration.
Part (a) — use F = EQF = 3.0 × 10⁴ × 1.60 × 10⁻¹⁹F ≈ 4.8 × 10⁻¹⁵ NPart (b) — use F = ma → a = F ÷ ma = 4.8 × 10⁻¹⁵ ÷ 9.11 × 10⁻³¹a ≈ 5.3 × 10¹⁵ m s⁻²A tiny force, but on such a tiny mass it’s a colossal acceleration — which is why electron beams bend so easily.
💡 Top tips
Parabola, not circle. An electric field gives a constant force (parabola, like a projectile); a magnetic field gives a circle — a favourite way to catch people out
Opposites attract: positive charges swing to the − plate, negatives to the + plate, and neutral particles aren’t deflected at all
Deflection ∝ q ÷ m at a fixed speed — heavy particles barely bend, light ones bend a lot
Faster = straighter. A quick particle spends less time in the field, so it has less time to be pulled aside
⚠ Common mistakes
Drawing a circular path in an electric field — the constant force makes a parabola
Bending the charge the wrong way — a positive charge goes toward the negative plate, not the positive one
Forgetting that a neutral particle passes straight through, undeflected
Thinking a heavier particle deflects more — greater mass means less deflection
Up next: we switch both fields on at once. Cross an electric field with a magnetic one and their forces can be set to cancel exactly — a “velocity selector” that lets only one speed of particle through in a straight line. That’s the final page of this topic.
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