IB DP Physics: Electric charge, Coulomb's law, electric and magnetic fields (DP Physics) – Revision Notes

These notes condense the standard level and higher level understandings of D.2, Electric and magnetic fields, from the IB Physics guide (first assessment 2025). The higher level potential content is covered in a separate unit. For full explanations read the study guide, then try the practice questions. Check what you already know with the free 10-minute diagnostics.

Also useful: the course hub and the printable checklist.

Key definitions

• Elementary charge, e: the smallest unit of free charge, 1.60 × 10⁻¹⁹ C. All charges are whole-number multiples of it.
• Electric field strength, E: force per unit positive test charge at a point. Vector; unit N C⁻¹ or V m⁻¹.
• Electric field line: a curve whose tangent gives the force direction on a small positive charge.
• Magnetic field line: a curve along which a free north pole would be pushed.
• Earthing (grounding): connecting a body to the Earth so that electrons can flow to or from it.

Formulas

Quantity	Equation	Notes
Coulomb’s law	F = k q₁q₂ / r²	Point charges; r is centre to centre
Constant	k = 1/(4πε₀)	About 8.99 × 10⁹ N m² C⁻²; ε₀ about 8.85 × 10⁻¹² F m⁻¹
Field strength	E = F/q	Direction of force on positive q
Point charge field	E = kQ/r²	Follows from F = kQq/r²; radial
Uniform field	E = V/d	Between parallel plates
Force on a charge in a field	F = qE	Rearranged E = F/q
Balanced drop	qE = mg	Millikan-type experiment

Forces between charges

• Like charges repel. Unlike charges attract.
• The two forces in a pair are equal in size and opposite in direction.
• F is proportional to q₁q₂ and to 1/r².
• Doubling a charge doubles F. Doubling r gives F/4. Halving r gives 4F.

Method: Coulomb’s law

1. Convert to coulomb and metre.
2. Substitute magnitudes of the charges and r.
3. State attraction or repulsion from the signs.
4. Give the force on each body (equal magnitudes).

Reminder: charges of 2.0 µC and 3.0 µC at 0.10 m give F = 8.99 × 10⁹ × 2.0 × 10⁻⁶ × 3.0 × 10⁻⁶ / 0.10² = 5.4 N.

Conservation of charge

• The total charge of an isolated system is constant.
• Identical conducting spheres that touch share their total charge equally.
• Reminder: −6.0 µC and +2.0 µC touch. Total = −4.0 µC, so each sphere ends with −2.0 µC.

Millikan’s experiment

• Charged oil drops are held between horizontal plates by adjusting the voltage.
• Balanced: qE = mg, so q = mg/E and E = V/d.
• Every result is a whole number of elementary charges. This is the evidence that charge is quantized.
• To find e from data: divide all values by a trial unit and look for whole numbers.
• Reminder: a drop of mass 3.3 × 10⁻¹⁵ kg is held between plates 1.0 cm apart with 2.0 kV across them. E = 2000 / 0.010 = 2.0 × 10⁵ V m⁻¹, so q = mg/E = (3.3 × 10⁻¹⁵ × 9.81) / 2.0 × 10⁵ = 1.6 × 10⁻¹⁹ C, which is one elementary charge.
• Reminder: a drop with 9.6 × 10⁻¹⁹ C carries 9.6 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 6 elementary charges.

Ways to charge a body

Method	What happens	Result
Friction	Electrons transfer between two rubbed insulators	Equal and opposite charges
Contact	Charge is shared on touching	Same sign as the charged body
Induction	Charges redistribute; earth the body; remove earth; remove charged body	Opposite sign to the charged body

Method: charging by induction

1. Bring the charged body near, without touching.
2. Connect the conductor to earth.
3. Disconnect the earth.
4. Remove the charged body.

Only electrons move in solids. A positive charge means missing electrons.

Electric field strength and lines

• E = F/q. A negative charge is pushed against E.
• Point charge: E = kQ/r², outwards for positive Q and inwards for negative Q.
• Line rules: start on positive and end on negative; never cross; arrows show direction; closer lines mean stronger field; meet conductor surfaces at right angles.
• Charged conducting sphere: charge sits on the surface; E = 0 inside; outside, the field is radial like a point charge at the centre.
• Two equal like charges: zero field at the midpoint. Two equal and opposite charges: fields add at the midpoint.

Worked reminders

Field of a pair: charges of +1.5 nC and −1.5 nC are 0.60 m apart in air. At the midpoint each is 0.30 m away, so each gives E = 8.99 × 10⁹ × 1.5 × 10⁻⁹ / 0.30² = 1.5 × 10² N C⁻¹, both pointing towards the negative charge. The total is 3.0 × 10² N C⁻¹.

Force from field: a particle of charge +3.2 × 10⁻¹⁹ C in a field of 2.0 × 10³ N C⁻¹ feels F = qE = 6.4 × 10⁻¹⁶ N in the direction of the field.

Parallel plates

• E = V/d, uniform between the plates and directed from the positive to the negative plate.
• Lines are parallel and evenly spaced in the middle and bulge outwards at the edges.
• Reminder: 600 V across 1.5 cm gives E = 600 / 0.015 = 4.0 × 10⁴ V m⁻¹. The force on an electron is 1.60 × 10⁻¹⁹ × 4.0 × 10⁴ = 6.4 × 10⁻¹⁵ N.

Magnetic field lines

Source	Pattern	Direction rule
Bar magnet	Closed loops, north out to south, closest at poles	Outside from N to S; inside from S to N
Straight wire	Concentric circles, further apart with distance	Thumb along current, fingers show field
Circular coil	Circles round the wire, straight through the centre	Fingers along current, thumb along the field at centre
Air-core solenoid	Uniform inside, bar magnet pattern outside	Fingers along current, thumb to north end

Dot (⊙) means out of the page and cross (⊗) means into the page. Current into the page gives clockwise field circles. Current out of the page gives anticlockwise circles.

Must-know distinctions

• Electric field lines begin and end on charges. Magnetic field lines form closed loops.
• Charge conservation concerns the total. Quantization concerns the size of each unit.
• Contact charging gives the same sign. Induction with earthing gives the opposite sign.
• Electron flow points opposite to conventional current. Grip rules use conventional current.

Quick self-test

1. Two protons are placed near each other. Is the force attractive or repulsive?
2. A force of 0.40 N acts between two charges. What is the force if r is tripled?
3. Find the force between 1.0 µC and 4.0 µC at 0.20 m apart.
4. An object gains 5.0 × 10¹² electrons. State its charge.
5. Identical spheres of −6.0 µC and +2.0 µC touch, then part. Find each final charge.
6. State what Millikan’s results showed about charge.
7. A 3.0 µC test charge feels a force of 4.5 mN. Find E.
8. Find E between plates 1.5 cm apart with 600 V across them.
9. Find the field strength 0.50 m from a +2.0 µC point charge.
10. State how field line spacing shows field strength.
11. A wire carries current out of the page. Give the sense of the field circles.
12. Which end of a solenoid is the north pole?

Answers

1. Repulsive (like charges).
2. Divided by 9: 0.40 / 9 = 0.044 N.
3. F = 8.99 × 10⁹ × 1.0 × 10⁻⁶ × 4.0 × 10⁻⁶ / 0.20² = 0.90 N (0.899 N).
4. q = −5.0 × 10¹² × 1.60 × 10⁻¹⁹ = −8.0 × 10⁻⁷ C.
5. Total = −4.0 µC, so −2.0 µC each.
6. Every measured charge was a whole-number multiple of one smallest value, so charge is quantized.
7. E = 4.5 × 10⁻³ / 3.0 × 10⁻⁶ = 1.5 × 10³ N C⁻¹.
8. E = 600 / 0.015 = 4.0 × 10⁴ V m⁻¹.
9. E = 8.99 × 10⁹ × 2.0 × 10⁻⁶ / 0.50² = 7.2 × 10⁴ N C⁻¹, directed away from the charge.
10. Closer lines mean a stronger field.
11. Anticlockwise.
12. The end where, looking at it, the current circulates anticlockwise (the end that field lines leave).

Where marks are usually lost

• Leaving charges in nC or µC, or distances in cm, inside Coulomb’s law.
• Squaring the distance incorrectly, or forgetting to square it at all.
• Giving only a magnitude for E or F when a direction was asked.
• Putting the sign of each charge into the formula and then misreading a negative answer.
• Writing that Millikan “found the charge of the electron” without saying all results were whole-number multiples.
• Describing induction without the earthing step, or in the wrong order.
• Field lines that intersect, lack arrows or end in empty space.
• Using electron flow in the right-hand grip rule.
• Claiming a field exists inside a charged conducting sphere.
• Treating a negative charge as feeling a force along E instead of against it.
• Quoting k or e without its unit, or giving answers to far too many significant figures.

Official syllabus

These notes follow the IB Physics guide, first assessment 2025, published by the International Baccalaureate Organization, sub-topic D.2.