Fields

Q: How do you calculate escape velocity?

Set total mechanical energy at the surface to zero: $\tfrac12mv^2 - \tfrac{GMm}{r}=0$, giving $v_{esc}=\sqrt{2GM/r}$.

Q: What's the difference between gravitational and electric fields?

Both follow a $1/r^2$ law, but gravity is always attractive (mass only ever attracts mass), while electric force can attract or repel depending on whether the charges have the same or opposite sign.

Gravitational and electric fields share one skeleton — master the parallel and Theme D falls into place

Diagram comparing gravitational field lines around a planet and electric field lines around a positive charge

Subject

Physics

Curriculum

IB Diploma Programme

Grade

Topic

Fields

Reading

7 min

Difficulty

Standard

Quick facts

Difficulty

★★★☆☆

Exam weight

Core SL theme — Paper 1 short answers + Paper 2 data question

Prerequisites

Circular motion, work & energy, vectors

You'll learn

g, E, V, escape speed, orbits, motion in E/B fields

Revision time

45–60 min

Fields is one of the four core SL themes in IB DP Physics, and it rewards students who spot the pattern rather than memorise separately. Gravitational field strength and electric field strength both fall off as $1/ r^{2}$ ; gravitational potential and electric potential both measure energy per unit mass or charge. Once you see that gravity is always attractive while electric force can attract or repel, most of the topic becomes applying one structure twice. This teaser covers the five ideas examiners test most: the field-strength-vs-potential distinction, gravitational fields and orbits, electric fields and Coulomb's law, magnetic force equations, and motion of charged particles in uniform fields. For full derivations, worked examples, and the complete formula sheet, the linked revision notes go deeper.

What you’ll be able to do

✓Distinguish field strength (vector) from potential (scalar)

✓Apply $g=GM/r^2$ and $V_g=-GM/r$ to planetary and satellite problems

✓Calculate escape speed and orbital period from energy and force balance

✓Apply Coulomb's law and compare it structurally to Newton's law of gravitation

✓Use $F=qvB\sin\theta$ and $F=BIL\sin\theta$ correctly, including the angle term

✓Determine the direction of magnetic force using right-hand rules for positive and negative charges

✓Predict parabolic motion in a uniform E field and circular motion in a uniform B field

Field Strength vs Potential: The Master Distinction

Field strength is a vector — it tells you the force per unit mass or charge and points in the direction a positive test object would accelerate. Potential is a scalar — it tells you the energy per unit mass or charge at a point, with no direction, and it's what you use for work-done calculations. Field lines show force direction; equipotential surfaces are always perpendicular to them and cost zero work to move along.

Field lines and perpendicular equipotential surfaces around a point mass

Exam tip

'State' questions usually want potential (a number); 'calculate the force on...' questions want field strength (a vector). Spot the keyword before you pick a formula.

Mini summary

Field strength = vector (force per unit mass/charge); potential = scalar (energy per unit mass/charge).

Gravitational Fields, Escape Speed and Orbits

Newton's law $F = G m_{1} m_{2} / r^{2}$ gives a spherical mass a radial field, exactly as if all its mass were concentrated at the centre — but only outside the sphere. Near Earth's surface the field looks locally uniform ( $g \approx 9.81 N kg^{- 1}$ ), while at satellite altitudes you must treat it as radial with $g$ decreasing as $r$ increases. Gravitational potential energy and potential are both defined as zero at infinity, forcing them negative everywhere else — a mass must gain energy to escape to infinity.

Satellite orbiting Earth with radius drawn from Earth's centre through its surface to the satellite

Quantity	Formula	Notes
Field strength	g = GM/r²	vector, points to centre
Potential	V_g = -GM/r	scalar, always negative
Escape speed	v = √(2GM/r)	from ½mv² + E_p = 0

Common mistake

Plugging the given height $h$ directly into $g = GM / r^{2}$ instead of $r = R_{pl an e t} + h$ — always write $r =$ as its own line of working.

Mini summary

Radius is always measured from the centre of mass; $E_{p}$ and $V_{g}$ are negative by definition, not by error.

Electric Fields and Coulomb's Law

Coulomb's law $F = k q_{1} q_{2} / r^{2}$ shares Newton's gravitation's exact $1/ r^{2}$ structure, but electric force can attract or repel depending on charge sign. Field lines point away from positive charges and into negative ones — always the direction a positive test charge would accelerate. Between oppositely charged parallel plates the field is uniform, giving constant field strength $E = V / d$ .

Field lines around positive and negative point charges, and uniform field between parallel plates

Exam tip

Unlike gravity, electric potential energy $E_{p} = k Qq / r$ can be positive or negative depending on the charges' signs — don't assume it's always negative like $E_{p}$ for gravity.

Mini summary

Same $1/ r^{2}$ skeleton as gravity, but sign of charge decides attraction or repulsion.

Magnetic Force on Charges and Currents

Magnetic fields need a moving charge or current — they're never produced by stationary charge alone, and their field lines always form closed loops with no monopoles. The force on a moving charge is $F = q v B sin θ$ , and on a current-carrying wire it's $F = B I L sin θ$ , where $θ$ is the angle between velocity (or wire) and the field. Right-hand rules give direction for conventional current or positive charge; for negative charge, work it out normally then reverse it.

Right-hand rule diagram showing force, velocity and magnetic field directions for a positive and negative charge

Common mistake

Writing $F = q v B$ or $F = B I L$ whenever an angle other than $90°$ is given — always check $θ$ before substituting; the $sin θ$ term is not optional unless perpendicularity is stated or implied.

Mini summary

Never drop $sin θ$ ; reverse right-hand-rule direction for negative charges.

Motion in Electric and Magnetic Fields

A charged particle in a uniform electric field feels a constant force along the field, giving constant acceleration $a = q E / m$ — combined with constant velocity perpendicular to the field, this produces projectile-style parabolic motion using the same suvat equations as mechanics. A charged particle moving in a uniform magnetic field feels a force always perpendicular to its velocity, so the force only bends the path, never speeds it up or slows it down — producing uniform circular motion instead.

Comparison of a charged particle's parabolic path in an electric field and circular path in a magnetic field

Exam tip

If a question mentions a magnetic field bending a particle's path without changing its speed, that's your cue: circular motion, not projectile motion.

Mini summary

Uniform E field → parabola (projectile motion); uniform B field → circle (constant speed, changing direction).

Quick formula sheet

F = \frac{G m _{1} m _{2}}{r ^{2}}

Newton's law of gravitation — Same shape as Coulomb's law, but always attractive

g = \frac{GM}{r ^{2}}

Gravitational field strength due to mass

M

V_{g} = - \frac{GM}{r}

Gravitational potential — always negative, zero at infinity

v_{esc} = \frac{2 GM}{r}

Escape speed from a planet's surface

T = 2 π \frac{r ^{3}}{GM}

Orbital period for a circular orbit

F = k \frac{q _{1} q _{2}}{r ^{2}}

Coulomb's law — repulsive or attractive depending on charge signs

E = \frac{V}{d}

Uniform electric field between parallel plates

F = q v B sin θ

Force on a moving charge in a magnetic field

F = B I L sin θ

Force on a current-carrying wire in a magnetic field

Practice questions

Easy

State whether gravitational field strength is a vector or scalar quantity, and justify your answer.
Write down Coulomb's law and identify one structural similarity with Newton's law of gravitation.
State why gravitational potential is always negative.

Medium

A satellite orbits at height $h$ above a planet's surface. Explain why the correct radius to use in $g = GM / r^{2}$ is $R_{pl an e t} + h$ , not $h$ alone.
A charged particle enters a uniform electric field moving perpendicular to it. Describe the shape of its path and explain why.
Explain why the force on a charge moving parallel to a magnetic field is zero, using $F = q v B sin θ$ .

Challenge

Derive the escape speed formula from the condition that total mechanical energy equals zero at infinity.
A charged particle moves in a circular path inside a uniform magnetic field. Explain why its kinetic energy stays constant even though a force acts on it continuously.
Compare the equations for gravitational potential and electric potential, explaining why one can be positive while the other cannot.

Frequently asked questions

What is the difference between field strength and potential in IB Physics?+

Field strength (g or E) is a vector giving force per unit mass or charge and has direction. Potential (V_g or V) is a scalar giving energy per unit mass or charge and has no direction — it's used for work-done calculations.

Why is gravitational potential always negative?+

Because the reference point is defined as zero at infinity, and any mass closer than infinity is in a bound, lower-energy state — so its potential must be negative relative to that zero.

How do you calculate escape velocity?+

Set total mechanical energy at the surface to zero: $\frac{1}{2} m v^{2} - \frac{GM m}{r} = 0$ , giving $v_{esc} = 2 GM / r$ .

What's the difference between gravitational and electric fields?+

Both follow a $1/ r^{2}$ law, but gravity is always attractive (mass only ever attracts mass), while electric force can attract or repel depending on whether the charges have the same or opposite sign.

When do you need sin theta in F=qvB?+

Whenever the velocity isn't stated (or clearly implied) as perpendicular to the magnetic field. Dropping $sin θ$ for a non-90° angle is one of the most common exam errors.

What path does a charged particle follow in a uniform magnetic field?+

A circular path at constant speed, because the magnetic force is always perpendicular to velocity and can only change direction, never speed.

Master Fields with the Complete IB DP Physics Revision Notes

Full derivations for escape speed, orbital mechanics, and field-potential relationships Worked examples covering common Paper 1 and Paper 2 traps Complete formula sheet with memory tricks for gravitational, electric, and magnetic fields Original mock papers and exam-style questions to build exam confidence

Get the Fields notes on RevisionPrep →

Physics: From Momentum to Relativity Physics: Wave Behaviour Physics: Why Matter Heats, Cools and Radiates Physics: Wave Behaviour — Rules and Formulas