IBDP Physics HL Cheat sheet - D.2 Electric and magnetic fields | IBDP Physics Cheatsheets

Electric charge and Coulomb’s law

Like charges repel and unlike charges attract.
Electric charge is conserved: total charge in an isolated system stays constant.
Coulomb’s law for point charges: $F = k\dfrac{q_1q_2}{r^2}$ , where $k = \dfrac{1}{4\pi\varepsilon_0}$ .
Force acts along the line joining the charges.
Inverse-square law: doubling $r$ makes force one quarter as large.
For exam questions, watch the sign of charge to decide attraction vs repulsion, but use magnitude in calculations.
A range of permittivity values may be needed, so do not assume vacuum unless stated.

This diagram shows the radial electric field around a single point charge. It is useful for linking field direction, symmetry, and the inverse-square weakening of field with distance. Use it to remember that field lines point away from positive and toward negative charges. Source

Charging methods and quantization of charge

Charge can be transferred by friction, contact, and electrostatic induction.
Grounding (earthing) allows excess charge to flow to or from Earth.
In induction, a nearby charged object causes charge separation without touching.
Millikan’s experiment provided evidence that charge is quantized.
Quantization means charge exists in discrete packets: $q = ne$ , where $n$ is an integer and $e$ is the elementary charge.
Exam wording often expects you to connect Millikan to the idea that all measured charges were integer multiples of $e$ .

This image shows Millikan’s oil-drop apparatus, used as evidence that electric charge is quantized. In IB Physics, the key takeaway is not the apparatus detail, but the conclusion that measured droplet charges came in whole-number multiples of $e$ . Source

Electric field strength and electric field lines

Electric field strength is force per unit charge: $E = \dfrac{F}{q}$ .
The direction of $E$ is the direction of the force on a positive test charge.
Field lines show field direction and relative strength.
Closer field lines = stronger field.
Field lines never cross.
Around a positive point charge, field lines point radially outward.
Around a negative point charge, field lines point radially inward.
For a conducting sphere, the field is perpendicular to the surface; inside a conductor in electrostatic equilibrium, $E=0$ .
You must be able to sketch and interpret fields for a single point charge, single spherical conductor, two point charges, and oppositely charged parallel plates, including edge effects.
Between parallel plates, the field is approximately uniform in the central region.
Uniform field between parallel plates: $E = \dfrac{V}{d}$ .

This diagram shows the uniform electric field between oppositely charged parallel plates, with slight edge effects near the ends. It is ideal for remembering why $E = \dfrac{V}{d}$ applies best in the middle region between the plates. Source

Magnetic field lines

A magnetic field is represented using magnetic field lines.
You must be able to sketch and interpret field patterns for a bar magnet, straight current-carrying wire, current-carrying circular coil, and air-core solenoid.
Magnetic field lines form closed loops.
Outside a bar magnet, field lines go from north to south.
For a straight current-carrying wire, use the right-hand grip rule to determine field direction.
For a solenoid, the field pattern is similar to a bar magnet.
Inside a solenoid, the field is relatively strong and uniform.
The exam often tests recognition of field patterns rather than long calculations.

This diagram shows the magnetic field pattern of a bar magnet. It helps you identify the characteristic looped field lines and compare magnetic fields with the electric field patterns you sketch for charges. Source

This diagram shows the field of an air-core solenoid, with nearly parallel field lines inside and curved lines outside. It is a strong visual link between a solenoid and a bar magnet field pattern. Source

HL only: electric potential energy and electric potential

Electric potential energy is the work done to assemble charges from infinite separation.
For two point charges: $E_p = k\dfrac{q_1q_2}{r}$ .
Sign matters: positive $E_p$ for like charges, negative $E_p$ for unlike charges.
Electric potential is a scalar quantity.
Electric potential at a point due to a point charge: $V_e = k\dfrac{Q}{r}$ .
Zero electric potential is defined at infinity.
Do not confuse electric potential $V_e$ with electric potential energy $E_p$ .
Link between them: potential = potential energy per unit charge.

HL only: potential gradient, work, and equipotentials

Electric field is the negative potential gradient: $E = -\dfrac{\Delta V_e}{\Delta r}$ .
The minus sign means electric field points in the direction of decreasing potential.
Work done moving a charge in an electric field: $W = q\Delta V_e$ .
Work in electric fields may be expressed in joules or electronvolts (eV).
No work is done when moving a charge along an equipotential surface.
Equipotential surfaces are always perpendicular to electric field lines.
Closer equipotential lines imply a stronger electric field.
You should recognize equipotentials for a point charge, up to four point charges, solid conducting sphere, hollow conducting sphere, and oppositely charged parallel plates.
Inside a conducting sphere in electrostatic equilibrium, potential is constant and field is zero.

This diagram shows electric field lines together with equipotential lines around a point charge. It is excellent for learning that field lines are perpendicular to equipotentials and that moving along one equipotential requires no work. Source

Common exam traps

Do not mix up field direction with the motion of a negative charge; the field is defined using a positive test charge.
Do not confuse electric field strength $E$ with force $F$ ; use $F=qE$ or $E=\dfrac{F}{q}$ as needed.
In Coulomb’s law, use centre-to-centre distance for spherical charged bodies treated as point charges.
Uniform field equations like $E = \dfrac{V}{d}$ apply to parallel plates, not to radial fields around point charges.
Potential is scalar; field is vector.
On equipotentials, work done is zero.
For conductors in electrostatic equilibrium, remember $E=0$ inside and the field at the surface is normal to the surface.

Checklist: can you do this?

Determine whether two charges attract or repel and calculate the force with Coulomb’s law.
Sketch and interpret electric field lines and magnetic field lines for all required syllabus cases.
Use $E = \dfrac{F}{q}$ and, for parallel plates, $E = \dfrac{V}{d}$ .
Explain how Millikan’s experiment supports quantization of charge.
For HL, use $V_e = k\dfrac{Q}{r}$ , $E = -\dfrac{\Delta V_e}{\Delta r}$ , and $W=q\Delta V_e$ and interpret equipotential diagrams.

Written by:

Dr Shubhi Khandelwal

Qualified Dentist and Expert Science Educator

Shubhi is a seasoned educational specialist with a sharp focus on IB, A-level, GCSE, AP, and MCAT sciences. With 6+ years of expertise, she excels in advanced curriculum guidance and creating precise educational resources, ensuring expert instruction and deep student comprehension of complex science concepts.