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. Here's the thing — it's frustrating. In practice, "Which of the following statements about magnetic fields are true? Even so, you know the basics: magnets have poles, field lines go north to south, moving charges create fields. 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. Because of that, you can't see it. You can't touch it. But you can measure its effect on moving charges, magnetic dipoles, and ferromagnetic materials.
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. On the flip side, no motion, no magnetic field. That's not a simplification. It's fundamental.
You'll probably want to bookmark this section.
The field isn't "lines" — lines are just a visualization tool
Textbooks draw field lines. They're useful. Think about it: 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. Even so, the field is continuous. Thinking of it as discrete lines leads to real misunderstandings — like believing the field is zero between the lines Not complicated — just consistent. Nothing fancy..
It's not Small thing, real impact..
Magnetic monopoles don't exist (as far as we know)
Every magnet you've ever held has a north and a south pole. Think about it: you get two smaller magnets, each with its own north and south. That said, in plain English: no sources, no sinks. Cut it in half? Magnetic fields don't work that way. Which means you can't isolate a single magnetic charge. Field lines form closed loops. Gauss's law for magnetism says the divergence of B is zero: ∇·B = 0. Practically speaking, electric fields come from positive and negative charges that can exist independently. Always It's one of those things that adds up. Which is the point..
Why It Matters / Why People Care
You interact with magnetic fields constantly. The motor in your fridge compressor. The generator at the power plant. But the hard drive (if you still have one). That said, the MRI machine that images your brain without radiation. Your phone's compass. Wireless charging. Induction cooktops No workaround needed..
Understanding which statements are true isn't academic trivia. Consider this: 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.
The cost of getting it wrong
Engineers have melted transformers by assuming the field stays inside the core. Which means (It doesn't — fringing fields are real. ) Students lose points claiming magnetic fields do work on charges. That's why (They don't — the force is always perpendicular to velocity. But ) Hobbyists build "free energy" devices misunderstanding Lenz's law. The misconceptions aren't harmless.
How Magnetic Fields Actually Work
Let's walk through the core principles. Still, 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.
Magnetic fields do zero work on free charges
Work = F · d. In real terms, force F is perpendicular to v. Displacement d is along v. Dot product is zero. Always And it works..
So how does a magnetic crane lift a car? But the field itself? Still does zero work. The field mediates the energy transfer. The field exerts forces on bound charges in the metal — electrons in atoms, aligned spins. The lattice does the work. This distinction matters in thermodynamics and Poynting vector analysis.
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. But same cross product. Same perpendicular force. This is how motors work — torque on a current loop in a uniform field But it adds up..
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.
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 Surprisingly effective..
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. In real terms, no beginning, no end. Which means Inside the magnet, they continue from south back to north. Always. In real terms, they form closed loops. If you draw them stopping at the poles, you're drawing it wrong That's the whole idea..
"The magnetic field inside a solenoid is zero"
Wrong. So b = μ₀nI. Worth adding: they don't. Outside it's nearly zero. Practically speaking, it's uniform and strong inside an ideal infinite solenoid. On the flip side, people confuse "outside" with "inside" — or they think the field cancels inside because contributions oppose. They add Practical, not theoretical..
"Magnetic force can speed up a particle"
Can't. Kinetic energy stays constant. It changes direction, not speed. Force is perpendicular to velocity. 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 Most people skip this — try not to..
