IB Physics HL Topic 4 — Force Fields Paper 1 & 2 parabolic path ~15 min read

Charged Particles in Electric Fields

Last page, a magnetic field spun a charge round in a perfect circle and never changed its speed. Now switch the magnet off and switch on an electric field between two parallel plates. Everything changes. The force no longer sits at right angles to the motion — it points the same way the whole time. The particle speeds up, and instead of a circle it traces a parabola. If that shape rings a bell, it should: this is exactly a ball thrown sideways off a cliff.

📘 What you need to know

A charged particle in an electric field feels a force F = qE that makes it move
A charge fired across a uniform field (between parallel plates) follows a parabolic path
A positive charge bends towards the negative plate; a negative charge bends towards the positive plate
The force is constant in size and always in the same direction — unlike the magnetic case
An uncharged particle (e.g. a neutron) feels no force and goes straight through
The motion splits in two: constant velocity along the plates, constant acceleration across them
This is the same physics as a projectile in gravity — just swap g for qE/m
Deflection is bigger for more charge and a stronger field; smaller for more mass and more speed
Unlike a magnetic field, this force does work: the speed and kinetic energy increase

The force on the charge

Put a charge in an electric field and it feels a force. That is what a field is — a region where a charge gets pushed. The size of the push is beautifully simple.

Force on a charge in a field F = qE F = force (N) • q = charge (C) • E = field strength (N C⁻¹)

For the parallel plates you meet in almost every exam question, the field between them is uniform, and its strength comes straight from the voltage and the gap:

Uniform field between parallel plates E = V / d V = voltage across the plates (V) • d = plate separation (m)

Here is the one line that unlocks the whole topic. The electric force points along the field, not across the motion. So if a charge flies sideways into the field, the force pushes it sideways-on — steady, unchanging, always the same way. That is the exact recipe for a projectile. Hold that thought; we cash it in below.

Why the path is a parabola

Fire a charge horizontally into the gap between two charged plates. Split what happens into two independent directions.

Along the plates (horizontal): no force acts this way, so the charge keeps a constant velocity
Across the plates (vertical): a constant force acts, so the charge picks up a constant acceleration

Constant velocity one way, constant acceleration the other — combine them and you get a parabola. It is the same shape a football makes, or a stream of water from a hose.

The field points straight down, so a positive charge is pushed down toward the negative plate, and a negative charge is pushed up toward the positive plate. Same field, mirror-image paths.

It really is just a projectile

Put a charge question and a “ball off a cliff” question side by side and they are the same problem wearing different clothes. Gravity gives a ball a constant downward acceleration g. The field gives a charge a constant sideways acceleration qE/m. Swap one for the other and every equation carries over.

Replace g with qE/m and a charge-in-a-field question becomes a projectile question you already know how to solve. Split it into horizontal and vertical, and away you go.

Horizontal
constant v

combine
with

Vertical
constant a = qE/m

gives a

Parabola

What changes the amount of bend?

Two things make a charge bend more: giving it more charge, or turning up the field — both increase the force. Two things make it bend less: more mass (harder to shift), or more speed (less time in the field before it shoots out the far side).

Same field, same charge, same entry point — only mass and speed differ. The heavier or faster particle barely bends; the light, slow one dives for the plate.

Increase…	Deflection	Why
Charge q	Bigger bend	Bigger force, F = qE
Field E (or voltage V)	Bigger bend	Bigger force, F = qE
Mass m	Smaller bend	More inertia; a = qE/m is smaller
Speed v	Smaller bend	Less time in the field before it exits

A neat catch: an uncharged particle — a neutron, say — sails straight through undeflected. No charge means F = qE = 0. Examiners love slipping a neutron into a beam of protons to see if you spot that it ignores the field entirely.

⚡ Working an electric-field deflection question

Find the field. Parallel plates? E = V/d, with d in metres.
Find the force, then the acceleration: F = qE, then a = F/m.
Split the motion. Horizontal: x = vt. Vertical: y = ½at².
Time in the field comes from the horizontal: t = (plate length) / v.
Direction? Positive bends to the negative plate; negative bends to the positive plate.
Sanity check the deflection y is less than half the gap — or the particle hits a plate.

WE 1

A proton enters midway between two horizontal parallel plates, travelling horizontally at 4.0 × 10⁵ m s⁻¹. The plates are 6.0 cm long and 4.0 cm apart, with a potential difference of 250 V across them. (a) Calculate the electric force on the proton. (b) Calculate its vertical deflection as it leaves the plates. (c) State which plate it deflects towards. (m_p = 1.67 × 10⁻²⁷ kg, q = 1.60 × 10⁻¹⁹ C)

(a) Step 1 — field, then force E = V/d = 250 / 0.040 = 6250 N C⁻¹ F = qE = (1.60 × 10⁻¹⁹)(6250) F = 1.0 × 10⁻¹⁵ N (b) Step 2 — acceleration, then split the motion a = F/m = (1.0 × 10⁻¹⁵) / (1.67 × 10⁻²⁷) = 5.99 × 10¹¹ m s⁻² time in field t = L/v = 0.060 / (4.0 × 10⁵) = 1.5 × 10⁻⁷ s y = ½at² = ½(5.99 × 10¹¹)(1.5 × 10⁻⁷)² y = 6.7 × 10⁻³ m = 6.7 mm (c) which plate? the negative plate — a positive charge is pulled toward it Check it survives the trip: 6.7 mm is less than half the 40 mm gap (20 mm), so the proton clears the plates without hitting one. Always run that check — if y came out bigger than d/2, the particle would have struck a plate first.

WE 2

An electron and a proton enter the same uniform electric field at the same point, with the same horizontal speed. (a) State, with a reason, whether they deflect towards the same plate or opposite plates. (b) Determine which is deflected more, and roughly by what factor. (m_p/m_e = 1840)

(a) same plate or opposite? The two carry opposite signs of charge. So the electric force on each points the opposite way. opposite plates — they bend apart (b) which bends more? Same field, same magnitude of charge, so the force is the same size on each. But deflection y ∝ a = qE/m, and y ∝ 1/m for equal force and time. yₖ / yₚ = mₚ / mₖ = 1840 the electron deflects about 1840× more The forces are identical, but the electron is roughly 1840 times lighter, so it accelerates 1840 times harder. That is why electron beams are so easy to steer with modest voltages — and why old TV tubes deflected electrons, not protons.

WE 3

(a) An electron sits in a uniform field of strength 3.0 × 10⁴ N C⁻¹. Calculate the force on it. (b) An electron then enters a field between plates 5.0 cm apart with 120 V across them. The plates are 4.0 cm long and the electron enters at 2.0 × 10⁷ m s⁻¹ along the middle. Find its deflection on leaving. (c) A neutron enters at the same point and speed — describe its path. (m_e = 9.11 × 10⁻³¹ kg, e = 1.60 × 10⁻¹⁹ C)

(a) force from F = qE F = eE = (1.60 × 10⁻¹⁹)(3.0 × 10⁴) F = 4.8 × 10⁻¹⁵ N (b) Step 1 — field, force, acceleration E = V/d = 120 / 0.050 = 2400 N C⁻¹ F = eE = (1.60 × 10⁻¹⁹)(2400) = 3.84 × 10⁻¹⁶ N a = F/m = (3.84 × 10⁻¹⁶) / (9.11 × 10⁻³¹) = 4.22 × 10¹⁴ m s⁻² Step 2 — split the motion t = L/v = 0.040 / (2.0 × 10⁷) = 2.0 × 10⁻⁹ s y = ½at² = ½(4.22 × 10¹⁴)(2.0 × 10⁻⁹)² y = 8.4 × 10⁻⁴ m = 0.84 mm (c) the neutron A neutron has no charge, so F = qE = 0. it goes straight through, undeflected 0.84 mm is comfortably inside the 25 mm half-gap, so the electron makes it out. And the neutron? The field simply doesn’t see it — no charge, no force, dead straight. A lovely one-mark giveaway if you’re paying attention.

One difference from the magnetic case

On the last page, a magnetic field did no work — the speed never changed. An electric field is not like that. Because the force has a component along the motion, it does do work, so the charge speeds up and its kinetic energy rises as it crosses the field. Keep the two straight in your head.

Think of it this way. A magnetic force is a friend who only ever nudges you sideways — you change direction but never get tired. An electric force pushes you along your path too, so it actually feeds you energy. Magnetic: constant speed, circle. Electric: speeding up, parabola. Two different rides.

💡 Top tips

Parallel plates? Get the field first: E = V/d, with d in metres.
Force then acceleration: F = qE, then a = F/m.
Treat it as a projectile: constant v along, constant a across. Split the two.
Get the time in the field from the horizontal: t = length / v.
Positive → negative plate. Negative → positive plate. Uncharged → straight through.
Always check y < half the gap, or the particle hits a plate.
Unlike a magnetic field, this one does work — the speed and KE go up.

⚠ Common mistakes

Leaving d in cm or mm in E = V/d. Convert to metres first
Saying the path is a circle — that’s the magnetic field. Here it’s a parabola
Thinking the speed stays constant. An electric field does work, so the charge speeds up
Sending a positive charge to the positive plate. Opposites attract — it goes to the negative one
Forgetting an uncharged particle feels no force and travels straight through
Using y = vt for the sideways bend. The sideways motion accelerates: y = ½at²
Assuming a heavier particle bends more. More mass means less deflection

Quick recap: A charge in an electric field feels a force F = qE, and between parallel plates the field is E = V/d. Fired across the field, it keeps a constant velocity along the plates but a constant acceleration across them, so it traces a parabola — exactly like a projectile with g swapped for qE/m. Positive charges bend to the negative plate, negative to the positive, and uncharged particles go straight through. Bend is bigger for more q or E, smaller for more m or v. And unlike a magnetic field, this force does work, so the charge speeds up.

Now put both fields together. Line up an electric field and a magnetic field so their forces oppose each other, and you can tune them until they exactly cancel. Only particles at one special speed sail through in a straight line — every other speed gets deflected out. That is a velocity selector, and it’s the heart of how J.J. Thomson weighed the electron. Next page: Charged Particles in Electric & Magnetic Fields.

Parabolas not clicking into place?

Book a free meeting and we’ll drill F = qE, the projectile split, and the “which plate, which way” rules until they’re automatic.

Book your free meeting

Charged Particles in Electric Fields

📘 What you need to know

The force on the charge

Why the path is a parabola

It really is just a projectile

What changes the amount of bend?

⚡ Working an electric-field deflection question

One difference from the magnetic case

💡 Top tips

⚠ Common mistakes

Parabolas not clicking into place?

Quick Links

Contact us

Follow us