You've probably seen those multiple-choice questions floating around physics forums or exam prep sites. " Then comes a list — some right, some wrong, some almost right but missing a crucial detail. It's frustrating. You know the basics: magnets have poles, field lines go north to south, moving charges create fields. Which means "Which of the following statements about magnetic fields are true? But the devil lives in the nuances.
Let's clear the noise. Here's what's actually true about magnetic fields — and what only sounds true.
What Is a Magnetic Field, Really
A magnetic field is a vector field. That means every point in space has a direction and a magnitude associated with it. You can't see it. You can't touch it. But you can measure its effect on moving charges, magnetic dipoles, and ferromagnetic materials And that's really what it comes down to..
Easier said than done, but still worth knowing.
The field exists around permanent magnets, sure. But it also appears around any moving electric charge — a current in a wire, an electron beam, even a spinning charged sphere. No motion, no magnetic field. That's not a simplification. It's fundamental It's one of those things that adds up..
The field isn't "lines" — lines are just a visualization tool
Textbooks draw field lines. They're useful. They show direction (tangent to the line) and relative strength (density of lines). But the lines themselves aren't physical. There's no "gap" between them. On the flip side, the field is continuous. Thinking of it as discrete lines leads to real misunderstandings — like believing the field is zero between the lines.
It's not.
Magnetic monopoles don't exist (as far as we know)
Every magnet you've ever held has a north and a south pole. Here's the thing — cut it in half? Also, you get two smaller magnets, each with its own north and south. You can't isolate a single magnetic charge. Electric fields come from positive and negative charges that can exist independently. Magnetic fields don't work that way. Gauss's law for magnetism says the divergence of B is zero: ∇·B = 0. On the flip side, in plain English: no sources, no sinks. Worth adding: field lines form closed loops. Always.
Why It Matters / Why People Care
You interact with magnetic fields constantly. The MRI machine that images your brain without radiation. The hard drive (if you still have one). In practice, wireless charging. Day to day, the generator at the power plant. Your phone's compass. Now, the motor in your fridge compressor. Induction cooktops.
Understanding which statements are true isn't academic trivia. Which means it's the difference between designing a working motor and burning one out. Between shielding an MRI room correctly and wasting thousands on ineffective materials. Between passing your E&M exam and... not No workaround needed..
The cost of getting it wrong
Engineers have melted transformers by assuming the field stays inside the core. (It doesn't — fringing fields are real.) Students lose points claiming magnetic fields do work on charges. Day to day, (They don't — the force is always perpendicular to velocity. ) Hobbyists build "free energy" devices misunderstanding Lenz's law. The misconceptions aren't harmless The details matter here..
How Magnetic Fields Actually Work
Let's walk through the core principles. That's why not analogies. The real physics.
The Lorentz force is the whole story for charges
A charge q moving with velocity v in a magnetic field B experiences a force:
F = q(v × B)
Cross product. That means:
- Force is perpendicular to both velocity and field
- Magnitude is |q|vB sin θ
- No force if the charge moves parallel to the field
- No force if the charge is stationary
This is non-negotiable. Every magnetic force on a free charge comes from this equation That's the part that actually makes a difference. Practical, not theoretical..
Magnetic fields do zero work on free charges
Work = F · d. Displacement d is along v. Force F is perpendicular to v. Worth adding: dot product is zero. Always Small thing, real impact..
So how does a magnetic crane lift a car? The field exerts forces on bound charges in the metal — electrons in atoms, aligned spins. On top of that, the lattice does the work. The field mediates the energy transfer. But the field itself? Still does zero work. This distinction matters in thermodynamics and Poynting vector analysis Small thing, real impact..
Current-carrying wires feel force, too
A wire is just moving charges in a lattice. The force on a segment dl carrying current I:
dF = I(dl × B)
Integrate along the wire. Same perpendicular force. Same cross product. This is how motors work — torque on a current loop in a uniform field.
The Biot-Savart law: fields from currents
Any steady current creates a magnetic field. For a current element I dl:
dB = (μ₀/4π) I (dl × r̂) / r²
Superposition applies. Integrate over the whole current distribution. This works for wires, loops, solenoids, arbitrary shapes. It's the magnetic analog of Coulomb's law — but with a cross product, so direction is trickier.
Ampère's law: the integral shortcut
For highly symmetric situations, you don't need to integrate Biot-Savart. Ampère's law:
∮ B · dl = μ₀ I_enc
The line integral of B around a closed loop equals μ₀ times the current passing through that loop. Works beautifully for:
- Infinite straight wire → B = μ₀I/2πr
- Infinite solenoid → B = μ₀nI inside, ~0 outside
- Toroid → B = μ₀NI/2πr inside
But — and this trips people up — Ampère's law always holds. It's just not always useful. Without symmetry, you can't pull B out of the integral Small thing, real impact..
Maxwell's correction: displacement current
Ampère's law as originally written failed for charging capacitors. No current between the plates, but there is a magnetic field. Maxwell added the displacement current term:
∮ B · dl = μ₀(I_cond + ε₀ dΦ_E/dt)
Changing electric flux acts like a current for producing magnetic fields. This symmetry — changing E makes B, changing B makes E — is why electromagnetic waves exist. Light is this mutual induction propagating through space.
Common Mistakes / What Most People Get Wrong
These show up on exams, in forums, and occasionally in bad textbooks.
"Magnetic field lines start at north and end at south"
Outside the magnet, yes. Inside the magnet, they continue from south back to north. They form closed loops. Which means always. So no beginning, no end. If you draw them stopping at the poles, you're drawing it wrong.
"The magnetic field inside a solenoid is zero"
Wrong. On top of that, it's uniform and strong inside an ideal infinite solenoid. B = μ₀nI. Outside it's nearly zero. People confuse "outside" with "inside" — or they think the field cancels inside because contributions oppose. They don't. They add Less friction, more output..
"Magnetic force can speed up a particle"
Can't. Force is perpendicular to velocity. It changes direction, not speed. Kinetic energy stays constant. If a particle speeds up in a magnetic field, something else is doing work — an electric field, a changing magnetic field inducing an electric field, or mechanical constraint forces Took long enough..
