Electric Field and Magnetic Field

Definition: Regions of space around charged particles or magnets where electric or magnetic forces act on other charges or magnetic materials.

How It Works

An electric field radiates outward from a charge; force on a test charge is F = qE, and the field itself exists whether or not another charge is present to feel it.
Electric field strength follows an inverse-square law from a point charge, growing with the source charge’s magnitude and weakening with the square of distance.
A magnetic field surrounds any moving charge (electric current) or arises from intrinsic magnetic moments in materials like permanent magnets.
Magnetic field lines always form closed loops with no beginning or end, unlike electric field lines, which start on positive charges and end on negative ones.
The magnetic force on a moving charge, the Lorentz force, is always perpendicular to both the charge’s velocity and the field, so it changes direction but never speed, meaning it does zero work.
Electric fields exert force on any charge, moving or stationary. Magnetic fields exert force only on moving charges (or on other magnets).
A changing magnetic field induces a circulating electric field (Faraday’s law), and a changing electric field contributes to a magnetic field (Ampere-Maxwell law); this mutual induction is what lets electromagnetic waves propagate through empty space.
When multiple sources are present, the total field at any point is the vector sum of each source’s individual field, the superposition principle.

Field Line Rules

Property	Electric field lines	Magnetic field lines
Start/end points	Start on + charges, end on − charges	Form closed loops, no start or end
Density meaning	Denser lines = stronger field	Denser lines = stronger field
Direction at a point	Tangent to the line, force direction on + test charge	Tangent to the line, defines B direction
Can lines cross?	Never	Never
Isolated source	Single + or − charge possible	Isolated N or S pole never observed

Illustration

Under the Hood

Key equations:

E = kQ / r²    (point charge field, k = 8.99 × 10⁹ N·m²/C²)

F = qE

B = μ₀I / (2πr)   (field from a long straight wire, μ₀ = 4π × 10⁻⁷ T·m/A)

F = qvB sinθ    (Lorentz force on a moving charge)

F = BIL sinθ    (force on a current-carrying wire)

Worked Example 1: Electric field from a point charge Given: Q = 5 μC (5 × 10⁻⁶ C), distance r = 0.1 m Step 1: E = kQ/r² = (8.99 × 10⁹)(5 × 10⁻⁶) / (0.1)² Step 2: E = (8.99 × 10⁹)(5 × 10⁻⁶) / 0.01 Answer: E ≈ 4.50 × 10⁶ N/C, directed away from the charge if Q is positive.

Worked Example 2: Force on a charge placed in that field Given: a second charge q = 2 μC placed at the same point, E = 4.50 × 10⁶ N/C Step 1: F = qE = (2 × 10⁻⁶)(4.50 × 10⁶) Answer: F ≈ 8.99 N, pushing the two positive charges apart.

Worked Example 3: Magnetic field around a current-carrying wire Given: current I = 10 A, distance r = 0.05 m from the wire Step 1: B = μ₀I/(2πr) = (4π × 10⁻⁷)(10) / (2π × 0.05) Step 2: B = (1.2566 × 10⁻⁵) / (0.3142) Answer: B ≈ 4.0 × 10⁻⁵ T = 40 μT, comparable in size to Earth’s own magnetic field.

Worked Example 4: Lorentz force on a moving proton Given: proton charge q = 1.6 × 10⁻¹⁹ C, speed v = 2 × 10⁶ m/s, field B = 0.5 T, velocity perpendicular to B Step 1: F = qvB = (1.6 × 10⁻¹⁹)(2 × 10⁶)(0.5) Answer: F ≈ 1.6 × 10⁻¹³ N, curving the proton into a circular path, the basis of how cyclotrons and mass spectrometers steer particles.

Worked Example 5: Force on a current-carrying wire in a field Given: field B = 0.3 T, current I = 5 A, wire length in the field L = 0.4 m, perpendicular orientation Step 1: F = BIL = (0.3)(5)(0.4) Answer: F = 0.6 N, the force that spins the rotor in every electric motor.

Worked Example 6: Electric field between parallel plates (capacitor) Given: parallel plate capacitor with voltage V = 12 V across a plate separation d = 0.002 m (2 mm) Step 1: Uniform field between plates: E = V/d Step 2: E = 12 / 0.002 Answer: E = 6000 V/m = 6000 N/C, uniform in direction and magnitude between the plates, unlike the inverse-square field of a point charge.

Why It Matters

Electric motors and generators both work by exploiting the force between current-carrying wires and magnetic fields, just in opposite directions of energy conversion.
MRI machines use magnetic fields of 1.5 to 3 Tesla, tens of thousands of times Earth’s field, to align hydrogen nuclei in the body for imaging.
Particle accelerators use electric fields to accelerate charged particles and magnetic fields to steer and focus them along circular or linear paths.
Electrostatic precipitators and photocopiers use charged surfaces and electric fields to attract and collect particles or toner.
Wireless communication depends entirely on oscillating electric and magnetic fields propagating as electromagnetic waves through space.
Compasses and magnetic navigation rely on Earth’s magnetic field, generated by convection currents in its molten iron core.
Capacitors, found in nearly every electronic circuit, store energy directly in the electric field between two charged plates.
Maglev trains use strong magnetic fields both to levitate above the track and to propel the train forward, eliminating rolling friction.

Common Pitfalls

Mixing up field direction with force direction for magnetic fields; the force is perpendicular to B, not parallel to it, unlike the electric field case.
Thinking a magnetic field does work on a moving charge; it only ever changes the direction of motion, never the speed, so kinetic energy stays constant.
Forgetting that fields exist in space independent of a test charge being present; the field is a property of the source, not something created by the charge that “feels” it.
Adding field magnitudes directly from multiple sources instead of adding them as vectors, which ignores direction and can give a wildly wrong total.
Confusing field strength (measured in N/C or V/m for E, tesla for B) with force itself (newtons).
Assuming magnetic monopoles exist; every magnet found in nature has both a north and south pole, no isolated pole has ever been observed.
Mixing up the tesla (SI unit) with the gauss (older CGS unit); 1 T = 10,000 G, a common source of off-by-10,000 errors.
Forgetting the sinθ term in the Lorentz force and current-carrying wire formulas; the force is maximum when velocity or current is perpendicular to the field and drops to zero when parallel to it.

Comparison

Property	Electric field	Magnetic field
Source	Stationary or moving charges	Moving charges (currents) or intrinsic spin
Acts on	Any charge, moving or stationary	Only moving charges (or other magnets)
Force direction	Parallel/antiparallel to the field	Perpendicular to both velocity and field
Does work on a charge?	Yes	No
Field line topology	Start/end on charges	Always closed loops
Monopoles	Isolated + or − charge exists	Never observed isolated

FAQ

Can an electric field exist without a magnetic field, or vice versa? Yes, for a stationary charge there’s only an electric field. But special relativity shows the split between “electric” and “magnetic” depends on the observer’s motion, so the two are really one unified electromagnetic field viewed differently from different reference frames.

Does Earth have both fields? Yes. Its magnetic field comes from convection in the molten iron outer core (the geodynamo), and a much weaker electric field exists in the atmosphere due to charge separation between the ground and ionosphere.

What actually is light, in terms of these fields? Light is a self-propagating electromagnetic wave: an oscillating electric field generates a perpendicular oscillating magnetic field, which regenerates the electric field, and so on, carrying energy through space without any medium.

Why doesn’t a magnetic field affect a stationary charge? The Lorentz force depends on velocity (F = qv×B); with v = 0, there’s no force at all, which is why magnets don’t attract or repel charges that aren’t moving relative to them.

How strong is Earth’s magnetic field compared to a refrigerator magnet? Earth’s surface field is about 25 to 65 microtesla, while a common refrigerator magnet is roughly 0.001 to 0.01 tesla, a hundred to a thousand times stronger at close range, even though Earth’s field extends for thousands of kilometers.

Example

An MRI (magnetic resonance imaging) machine surrounds a patient with a powerful, extremely uniform static magnetic field to align hydrogen nuclei in the body’s water and fat. It then applies precisely timed radio-frequency electromagnetic pulses to knock those nuclei out of alignment, and detects the electromagnetic signal they emit as they relax back, building a detailed image without ionizing radiation.

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