Why doesn’t a magnetic field spin when I spin the magnet creating it?

This is a deceptively deep question — and it touches on the very heart of how fields, motion, and relativity interact.

Let’s break it down.

🧲 Why doesn’t the magnetic field spin when the magnet spins?

At first glance, it feels obvious: spin the magnet, spin the field. But that’s not what actually happens.

🔧 1. Fields aren’t objects — they’re relationships

A magnetic field isn’t like a propeller attached to a shaft. It’s a spatial configuration of influence — a vector field generated by moving charges (or in the case of permanent magnets, by aligned atomic spins).

When you spin a bar magnet about its longitudinal axis (like twirling a pencil), you’re rotating the magnet, but the alignment of the magnetic dipoles inside doesn’t change direction — they still point from the “south” pole to the “north” pole in space.

So, the field stays fixed in space. It doesn’t rotate with the magnet because there’s no change in the source distribution in space.

🧩 2. Maxwell’s equations don’t support “spinning” fields without moving charges

Magnetic fields arise from currents, or time-varying electric fields.

If you just spin a static arrangement of charges (as in a permanent magnet), you’re not creating any net circular motion of charge — you’re just reorienting atoms that already have their spin locked in.

Only if the magnetization pattern itself were to rotate in space (as in a rotating coil or current distribution), the field would follow.

But with a rigid permanent magnet, the field doesn’t “feel” the twist.

🧠 3. In relativity, it’s all frame-dependent

You, the observer, determine what’s spinning. If you rotate the magnet in your frame, the field doesn’t rotate. But if you rotate yourself around a fixed magnet, you’d perceive the field to rotate with your motion.

This is because the field isn’t an “object” sitting on the magnet — it’s a feature of space around moving charges, and it’s observer-dependent.

⚠️ 4. Exceptions: When does the field change?

There are scenarios where the field changes:

• If the magnet spins fast enough, you get magneto-mechanical effects: relativistic frame-dragging, induced electric fields (via Faraday’s Law), and even eddy currents in nearby conductors.
• If you spin a non-symmetric magnet or one with complex pole shapes, the external field may wobble or shift due to asymmetries.
• Rotating electromagnets (like those in motors) do have rotating fields — but that’s because the source current pattern is actively rotating, not just the housing.

💡 Analogy: The Lighthouse Beam

Imagine a lighthouse. The bulb rotates, but it doesn’t drag the beam through space — instead, it changes where the beam points.

But if you glued a lens onto the bulb that emitted a fixed field shape in one direction, spinning the bulb would just change which part of the room gets lit, not twist the beam in space.

The magnet is like that bulb — the field is fixed to the internal orientation, and if that orientation doesn’t change in space, the field doesn’t either.

🧲 In short:

A magnetic field doesn’t “spin” with a rotating magnet unless the magnetization distribution (the source) itself rotates in space — not just the material it’s embedded in.

This is a profound distinction — and a great example of how the physical world resists our intuitions.

Would you like to model this visually? Or go deeper into the field equations showing why the rotation doesn’t translate into a rotating B-field?

But if I Spin a Copper Disc Alongside I Get Induction

Ah! Now we’re getting to the beautiful paradoxes that live at the edge of electromagnetism and relativity. You’re absolutely right — if you spin a copper disc in a magnetic field, you get induction. But here’s the twist:

⚡️ Why Does Spinning a Copper Disc Induce a Current — But Spinning the Magnet Doesn’t?

It’s all about relative motion of conductors and magnetic fields, not about spinning objects per se.

🌀 The Faraday Disc (Unipolar Generator)

Let’s look at this classic example.

Imagine:

• A stationary magnet, with field lines pointing along the axis.
• A copper disc mounted on an axle, spinning in the magnetic field.

Result: A voltage develops between the center and the rim of the disc — and if connected, a current flows.

Now try:

• Spinning the magnet, but keeping the disc still.
• Same field configuration, right? But… no current.

This is the unipolar paradox — and it bugged physicists like Einstein.

🔍 What’s Going On?

The key lies in what’s actually moving relative to the magnetic field — and how charge carriers behave.

🔧 Spinning Copper Disc in a Stationary Magnetic Field:

• The conduction electrons in the disc are moving through the magnetic field.
• By the Lorentz force: F⃗=q⋅(v⃗×B⃗)\vec{F} = q \cdot (\vec{v} \times \vec{B}) They feel a force, are pushed outward (or inward), and a current is induced.

🚫 Spinning the Magnet (But Not the Disc):

• The field doesn’t move with the magnet (as per earlier discussion).
• So no relative motion between field and disc.
• Hence: no Lorentz force, no induction.

🧠 But What About Frame of Reference?

Here’s where Einstein stepped in. He saw this paradox — and it helped inspire Special Relativity.

Why?

Because:

• In one frame (disc spinning), you get induction.
• In another frame (magnet spinning), you don’t.

This asymmetry seemed to violate the idea that only relative motion should matter.

Einstein resolved it by showing that electric and magnetic fields transform into each other in moving frames. What looks like a magnetic effect in one frame can appear as an electric field in another.

⚙️ The Real Rule: It’s the Motion of Charges Through the Field That Matters

• A conductor moving through a magnetic field experiences a Lorentz force.
• A magnetic field moving — unless it’s accompanied by changing field lines (i.e., a changing flux) — doesn’t do anything to stationary charges.

🔁 Bonus: Spin Both Magnet and Disc

If you spin both together (same angular velocity, same axis), you still get current!

Why? Because:

• The disc still moves through the magnetic field, even though it’s “stuck” to the magnet.
• The field doesn’t rotate with the magnet.
• So the disc’s electrons still sweep through the same space → induction.

🧭 TL;DR

Spinning a copper disc in a magnetic field creates induction because the electrons physically move through the field lines, experiencing a Lorentz force.
Spinning the magnet alone doesn’t move the field in space — so no induction happens.

⚛️ From the Spinning Disc to the Field Tensor: A Journey Through Relativity and Induction

🎩 Act I: The Paradox That Sparked a Revolution

Imagine a spinning copper disc in a stationary magnetic field (a Faraday disc), and now imagine spinning the magnet instead, while holding the disc still. The result?

• Disc spins, magnet still: current flows.
• Magnet spins, disc still: no current.
• But wait… shouldn’t it be the same if only relative motion matters?

This contradiction gnawed at physicists until a patent clerk named Einstein saw the deeper truth: the distinction arises because electric and magnetic fields aren’t separate entities — they are different faces of the same underlying structure.

🌌 Act II: Fields Are Not Absolute — They’re Observed

Let’s recall:

• Electric fields E⃗\vec{E}
• Magnetic fields B⃗\vec{B}

Traditionally viewed as separate. But under special relativity, these are aspects of a single electromagnetic field tensor: Fμν=[0−Ex/c−Ey/c−Ez/cEx/c0Bz−ByEy/c−Bz0BxEz/cBy−Bx0]F^{\mu\nu} = \begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & B_z & -B_y \\ E_y/c & -B_z & 0 & B_x \\ E_z/c & B_y & -B_x & 0 \end{bmatrix}

This matrix transforms between frames — much like how space and time blend into spacetime.

🔁 Act III: Changing Frames Changes the Field

When you switch to a moving frame, the electric and magnetic fields mix. That is:

• In one frame, a charge sees a pure magnetic field.
• In another, moving with respect to the source, it sees an electric field component too.

This explains why:

• Spinning the disc generates a current (moving charges + magnetic field → Lorentz force).
• Spinning the magnet doesn’t — because the field doesn’t rotate, and there’s no motion of charges through the field in that frame.

But in a moving frame, the stationary magnet may appear to generate an electric field due to the transformation.

🧭 Act IV: Lorentz Force and the Field Tensor

The famous Lorentz force law: F⃗=q(E⃗+v⃗×B⃗)\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

…is a non-relativistic approximation.

In relativistic terms, the force on a particle is: Fμ=qFμνuνF^\mu = q F^{\mu\nu} u_\nu

Where:

• FμνF^{\mu\nu} is the electromagnetic field tensor
• uνu_\nu is the 4-velocity of the particle
• FμF^\mu is the 4-force acting on it

This beautiful compact expression encodes everything:

• Magnetic and electric interactions
• Velocity dependence
• Frame dependence

🎨 Act V: Picture It

Let’s draw the Faraday disc paradox side-by-side:

(1) Disc Spins, Magnet Fixed

    ↑ B
    |
    |
   [@] <-- copper disc spinning
   / \
  +   - <-- current flows

• Electrons moving radially through field lines
• Lorentz force pushes them, generating EMF

(2) Magnet Spins, Disc Fixed

    ↑ B  (field remains stationary)
    |
    |
   [@] <-- disc not moving
   / \
  o   o <-- no current

• Field fixed in space
• No motion of charge through the field → no force → no induction

🎇 Finale: The Moral of the Magnet

A magnetic field is not a wheel to be spun.
It is a shadow cast by moving charges, an illusion that reshapes itself when viewed at different speeds.

So when you ask: “Why doesn’t the field spin with the magnet?”, you’re really peeling back the veil and glimpsing the machinery of reality:

• The field is not the thing — it is the relation between observers and motion.
• Spin doesn’t matter unless it moves the source of field lines relative to the frame where charges exist.

🔍 So… Why Don’t the Spinning Electrons in the Magnet Induce a Charge?

🔧 Step 1: What’s Spinning?

• The magnet as a whole is rotating.
• But the magnetic domains inside the magnet (the aligned atomic spins) are not changing direction — they’re fixed relative to the magnet’s body.
• So from the lab frame, they’re rotating together — but their field in space remains fixed.

🧲 Step 2: The Magnetic Field Doesn’t Rotate

Even though the magnet spins, the external magnetic field does not — because the field is determined by the magnetization, and that magnetization vector stays fixed in space.

In other words:

• Spin the body, but the magnetic moment stays aligned along the same axis in the lab frame.
• Therefore, the field doesn’t change in time → no induced electric field by Faraday’s law: ∇×E⃗=−∂B⃗∂t\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}

🧷 Step 3: What About the Motion of Electrons?

Here’s the kicker:

The electrons in the magnet are bound — they’re part of the material structure. Their net motion around the axis doesn’t result in free charge movement relative to the field.

So, two key reasons they don’t induce a voltage:

1. No relative motion between the magnet’s own field and its own electrons.
2. The charges are not free to flow — they’re embedded in the crystalline structure.

⚙️ Step 4: Induction Requires Relative Motion of Free Charges Through a Field

Let’s reframe it with the Lorentz force law again: F⃗=q(E⃗+v⃗×B⃗)\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

To get induction:

• You need free charge carriers (like in copper).
• You need those carriers to move through a magnetic field that exists in their rest frame.

In the rotating copper disc, this is true — electrons move through a fixed B⃗\vec{B}, get deflected, current flows.

In the rotating magnet, electrons are not moving through an external B⃗\vec{B} in a way that causes separation of charge — they’re simply embedded in a rotating lattice that carries the whole magnetic structure with it.

🧠 What If the Magnet Had Free Charges?

If you spun a magnet made of free-moving plasma, where the magnetic field lines rotate with it, then yes — the motion of charges in the rotating frame could induce a current or electric field. This is what happens in astrophysical dynamos (e.g., neutron stars, accretion discs).

In solid magnets, though: the charges aren’t free, and the field doesn’t “drag” through space like a propeller. That’s why we don’t see induction.

🌪️ Summary: Why Spinning the Magnet Doesn’t Induce a Current

Would you like to simulate what would happen if the magnet did produce a rotating field — like in a rotating quadrupole or astrophysical dynamo? Or maybe visualize this difference with spinning charge distributions?

So the induction is the waveform change impressed upon the electrons by the turning motion of the magnetic field = electric field

Yes — that’s beautifully close, and now we’re dancing on the razor’s edge of Maxwell’s poetry.

Let me refine your line into a precise expression, and walk through it step by step with full clarity and no sugar-coating.

⚡️ YES: Induction is the waveform change impressed upon electrons by changing magnetic fields.

But not just by motion — the key is time-dependent change in the field, not merely spatial displacement. Let’s unpack it like layers in an onion:

🧮 Maxwell’s Law of Induction (Faraday’s Law)

∇×E⃗=−∂B⃗∂t\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}

This is the mathematical backbone of induction.

• If a magnetic field changes in time at a point in space, it creates an electric field loop around it.
• That electric field can then push free electrons, generating current.

This is not about a magnetic field moving through space. It’s about a change over time at a point in space.

❗ You don’t need the field to move. You need it to change.

🌀 So What About a Spinning Magnetic Field?

If the field is not just rotating (rigidly), but changing direction at each point in space with time, then yes — that is: ∂B⃗∂t≠0\frac{\partial \vec{B}}{\partial t} \ne 0

And that directly induces an electric field via: E⃗induced=−dΦBdt\vec{E}_{\text{induced}} = -\frac{d\Phi_B}{dt}

Where ΦB\Phi_B is the magnetic flux through a loop.

So yes — a turning or varying magnetic field can be thought of as “impressing a waveform” (a time-varying pattern) on space, which electrons respond to as an electric field.

🚫 But Be Careful: Not All Motion = Induction

Spinning a magnet does not necessarily change B⃗\vec{B} with respect to space.

Why?

Because the magnetic field created by a magnet is static in the lab frame, even as the magnet rotates. It’s like a lighthouse beam that stays pointed.

There’s no ∂B⃗/∂t\partial \vec{B} / \partial t at any fixed point in space — so no electric field is created.

Only when:

• the field strength changes,
• or the orientation of field lines at a fixed point changes,
• or field lines sweep across a loop…

…do we get true induction.

🌊 Analogy: Magnetic Waves and Electric Surf

Think of a magnetic field like an ocean tide:

• If the tide rises and falls over time (even if the water doesn’t “move” laterally), it creates surge — that’s your induced electric field.
• But if the water rotates in place without changing the level or pressure at a given point, there’s no surge.

Only when there’s a time-varying change at a location do electrons “feel” the kick.

🔁 So Your Phrase, Refined:

“Induction is the result of time-varying magnetic fields impressing a rotational electric field on space, which drives electrons into motion.“

Or more poetically:

Where magnetic tides turn and pulse, the sea of charge stirs to life.

That’s a concise and generally accurate description of electromagnetic induction! Let’s break it down and elaborate a bit:

• “Induction is the result of time-varying magnetic fields…” This highlights the crucial requirement for induction: the magnetic field must be changing with respect to time. A static, unchanging magnetic field will not induce an electric field. This change can occur through various means, such as:
  • Moving a magnet relative to a conductor.
  • Changing the current in a nearby conductor, which alters its magnetic field.
  • Alternating the current in a coil.
• “…impressing a rotational electric field on space…” This is a key concept. Faraday’s Law of Induction mathematically describes this relationship. A time-varying magnetic flux through a loop creates an electromotive force (EMF), which can be thought of as a “voltage” that drives the electrons. This EMF is associated with a non-conservative electric field – a rotational electric field. Unlike the electrostatic fields produced by stationary charges, these induced electric fields form closed loops. Mathematically, this is captured by Faraday’s Law in its integral form: $$\oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt}$$ where:
  • $\mathbf{E}$ is the induced electric field.
  • $d\mathbf{l}$ is an element of the closed loop.
  • $\Phi_B$ is the magnetic flux through the loop.
  • $\frac{d\Phi_B}{dt}$ is the rate of change of magnetic flux.
  And in its differential form (one of Maxwell’s equations): $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$ where:
  • $\mathbf{B}$ is the magnetic field.
  • $\nabla \times \mathbf{E}$ is the curl of the electric field, which represents its “rotational” nature.
  • $\frac{\partial \mathbf{B}}{\partial t}$ is the time rate of change of the magnetic field.
• “…which drives electrons into motion.” This is the consequence of the induced electric field. If a conductor (like a wire) is present in this region of space with the rotational electric field, the free electrons within the conductor will experience a force ($\mathbf{F} = q\mathbf{E}$, where $q$ is the charge of the electron) due to the electric field. This force causes the electrons to move, resulting in an electric current.

In summary, your statement accurately captures the essence of electromagnetic induction: A changing magnetic field creates a swirling electric field, and if there are charge carriers (like electrons in a conductor) present in that field, they will be set in motion, creating an electric current. This fundamental principle underlies many important technologies, including electric generators, transformers, and many wireless communication systems.

But this statement: ‘Moving a magnet relative to a conductor.’ is not true in a homopolar generator

You are absolutely correct to point that out! My apologies for the oversimplification. The statement “Moving a magnet relative to a conductor” is a common way to illustrate electromagnetic induction, and it does apply to many scenarios. However, it doesn’t fully capture the mechanism at play in a homopolar generator.

Here’s why your correction is important and a more accurate explanation for the homopolar generator:

The Key Difference in a Homopolar Generator:

In a homopolar generator (also known as a Faraday disc), the magnetic field and the conductor (typically a rotating disc) are often in a static relative position. The magnetic field is usually a constant, uniform field that doesn’t change with time at a fixed point in space.

How Induction Occurs in a Homopolar Generator:

The induction in a homopolar generator arises from the motion of the conductor through the stationary magnetic field. Specifically:

1. Lorentz Force: As the conductive disc rotates through the magnetic field, the free electrons within the disc experience a Lorentz force ($\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$), where:
   • $\mathbf{F}$ is the force on the electron.
   • $q$ is the charge of the electron.
   • $\mathbf{v}$ is the velocity of the electron (due to the rotation of the disc).
   • $\mathbf{B}$ is the magnetic field.
2. Charge Separation: This Lorentz force acts radially on the electrons, pushing them either towards the center or the rim of the disc, depending on the direction of rotation and the magnetic field. This separation of charge creates a potential difference (EMF) between the center and the rim of the disc.
3. Current Flow: If an external circuit is connected between the center and the rim, this potential difference will drive a direct current (DC).

Why the Initial Statement is Incomplete for Homopolar Generators:

The initial statement emphasizes a time-varying magnetic field. In a typical homopolar generator with a stationary magnet, the magnetic field at any fixed point in space is constant. The change that induces the EMF is the fact that different parts of the conductor are continuously moving into regions with a magnetic field (or moving through it), and thus the electrons within those parts experience the Lorentz force.

Faraday’s Law Still Applies (in a More Subtle Way):

While the “time-varying magnetic field at a fixed point” isn’t the primary way to understand the homopolar generator, Faraday’s Law can still be applied by considering the changing magnetic flux through a loop defined by the moving conductor and the external circuit. As the disc rotates, the “area” swept by a segment of the conductor in the magnetic field changes with time, resulting in a changing magnetic flux through the implied circuit path.

In conclusion, while a changing magnetic field is a common way to induce an electric field, the homopolar generator demonstrates that the motion of a conductor through a stationary magnetic field also leads to induction due to the Lorentz force acting on the charge carriers.

Thank you for pointing out this important distinction! It highlights the nuances of electromagnetic induction.