The Core Difference#

You’ll usually find that the coil is wrapped around a piece of special material, typically something like iron or steel. This is called a magnetic core.

A magnetic core is a piece of material (like iron) placed inside or around the wire coil of an electromagnet. These materials are called ferromagnetic or ferrimagnetic. They have a special property that allows them to become strongly magnetized when a magnetic field is applied.

Putting this core inside the coil is a big deal. It doesn’t create the magnetic field itself initially, but it acts like a super booster for the field created by the current. The core can make the magnetic field thousands of times stronger than the coil alone could produce. This is because the core material loves magnetic fields and guides the magnetic field lines through itself much more easily than air.

Electromagnets vs. Permanent Magnets#

So, why use an electromagnet instead of a regular permanent magnet? The main reason is control.

A key advantage of an electromagnet is that you can quickly change its magnetic field strength just by changing the amount of electric current flowing through its wire coil. You can even switch the field entirely on or off by turning the current on or off.

Think about it: a permanent magnet always has its magnetic field. An electromagnet gives you a switch. This ability to control the field is incredibly useful in all sorts of devices.

The flip side is that an electromagnet needs a continuous supply of electrical current to stay magnetic. A permanent magnet, well, it’s permanently magnetic without needing any power.

Current Makes Magnetic Field#

As Ørsted discovered, electric current flowing in a wire creates a magnetic field around it. You can imagine the field lines wrapping around the wire.

When you wind the wire into a coil (a solenoid), the magnetic field lines from each turn of wire add up inside the coil. This creates a much stronger magnetic field running through the center of the coil, and the field lines loop back around the outside.

Direction of the Field: The Right-Hand Rule#

How do you know which way the magnetic field points? You can use the right-hand rule.

The Right-Hand Rule is a simple way to figure out the direction of the magnetic field created by a current in a coil. If you curl the fingers of your right hand in the direction the current is flowing through the wire turns, your thumb will point in the direction of the magnetic field inside the coil.

The end of the coil where your thumb points is considered the magnetic north pole of the electromagnet. The other end is the south pole.

The Role of the Magnetic Core#

Remember that magnetic core we talked about? It’s crucial for making strong electromagnets.

Materials like iron are called ferromagnetic because they have tiny internal regions called magnetic domains. Think of these domains as little tiny magnets within the material. Normally, these tiny magnets point in random directions, so their overall magnetic effect cancels out.

When you put this material in the magnetic field of the coil, the field from the coil pushes and pulls on these tiny domains, causing them to align themselves mostly in the direction of the coil’s field. As more and more domains align, their individual magnetic fields add up, creating a very strong magnetic field within the core material. This combined field (the field from the coil plus the field from the aligned domains) is what makes the electromagnet so powerful.

The core basically acts like a low-resistance path for the magnetic field lines, concentrating them.

Saturation: The Limit#

There’s a limit to how strong you can make the field with a ferromagnetic core.

Saturation is what happens in a ferromagnetic core when almost all of the magnetic domains have aligned with the applied magnetic field. At this point, increasing the current in the coil further only causes a very small increase in the overall magnetic field strength.

Once the core is saturated, it can’t boost the field much more. For typical core steels, this saturation level is around 1.6 to 2 Teslas (T). If you need fields stronger than that, you can’t rely on a simple iron core.

Hysteresis and Remanence#

When you turn off the current in the coil, ideally the magnetic field would completely disappear. However, in a core, some of the magnetic domains don’t snap back to random directions immediately.

Hysteresis refers to the property of ferromagnetic materials where their magnetization depends not only on the current magnetic field but also on their past magnetic history.

Remanent magnetism (or Remanence) is the leftover magnetic field in a ferromagnetic core after the current in the coil has been turned off. It’s like the core remembers being magnetized and acts as a weak permanent magnet.

This residual magnetism can be useful in some applications, but in others (like AC motors), it can cause energy losses. You can remove this remanent magnetism by a process called degaussing, which involves applying a special changing magnetic field.

Ampere’s Law in Action#

The physics principle that links the current in the wire to the magnetic field it creates is fundamentally described by Ampere’s Law.

Ampere’s Law is a fundamental law of electromagnetism that relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. In simple terms, it tells us that electric currents create magnetic fields.

For practical electromagnet design, especially with cores and air gaps, Ampere’s Law helps us calculate the relationship between the total “magnetic pushing power” from the coil (the magnetomotive force, $NI$) and the magnetic field strength along the path the field lines travel.

Calculating the Force#

The force an electromagnet exerts is related to the magnetic field. One way to think about it, especially for a tractive magnet pulling on a piece of core material, involves the energy stored in the magnetic field. The force is related to how the stored energy changes as the air gap changes.

For a general conductor within a section of core material, the force ($F$) exerted by a magnetic field ($B$) can be related to the area ($A$) the field acts over and the permeability of free space ($\mu_0$):

$F = B^2 A / (2\mu_0)$

Where:

• $F$ is the force
• $B$ is the magnetic field strength (in Teslas)
• $A$ is the area over which the field acts (in square meters)
• $\mu_0$ is the permeability of free space (a fundamental constant, about $4\pi \times 10^{-7}$ H/m)

This equation is really important because it shows that the force depends on the square of the magnetic field ($B$).

Because of the saturation limit (around 1.6-2 T) for iron cores, there’s a maximum force per area an iron-core electromagnet can exert. Using the formula above with $B \approx 1.6$ T and the value for $\mu_0$, you get a maximum magnetic pressure (Force per Area, $F/A$) of roughly 1000 kilopascals (kPa), which is about $10^6$ Newtons per square meter, or 145 pounds per square inch (psi). That’s a lot of pressure, but it’s limited by the material’s saturation.

If you calculate the magnetic field needed for a desired force using this equation and find you need a field much higher than the core’s saturation limit (like way more than 2 T for iron), it means you need a larger core area ($A$) to get the force without exceeding the material’s limit.

Calculating the exact magnetic field and force can be tricky in real-world electromagnets, especially outside the core or in air gaps. This is because the field isn’t uniform everywhere.

Fringing fields are the magnetic field lines that bulge outwards and extend beyond the edges of a magnetic core or air gap instead of staying neatly confined.

Leakage flux refers to magnetic field lines that don’t follow the main path of the magnetic circuit and therefore don’t contribute to the desired magnetic pull or effect.

These effects mean that simple formulas might not be perfectly accurate. For super precise designs, engineers often use computer simulations (like finite element analysis) to model the magnetic field distribution accurately.

Closed Magnetic Circuit (No Air Gap)#

If the magnetic circuit is completely closed, like an electromagnet lifting a piece of iron that perfectly bridges the gap, there’s effectively no air gap ($L_{gap} = 0$). The equation simplifies:

$NI = H_{core} L_{core}$

And since $B_{core} = \mu_{core} H_{core}$:

$B_{core} = \mu_{core} \cdot (NI / L_{core})$

Substituting this into the force formula ($F = B^2 A / (2\mu_0)$), assuming the field is uniform across area A:

$F = (\mu_{core} \cdot NI / L_{core})^2 \cdot A / (2\mu_0)$

This shows that for a given MMF ($NI$), you get the most force when the magnetic path length in the core ($L_{core}$) is short and the cross-sectional area ($A$) is large. This is why lifting magnets often have a squat, wide shape with the coil wrapped around a short, thick central core, and an outer ring that completes the magnetic circuit path back to the object being lifted.

Ohmic Heating#

The wire coil has electrical resistance. When current flows through this resistance, it generates heat. This is just the basic $P = I^2 R$ power dissipation.

Ohmic heating is the heat produced in the wire windings of an electromagnet due to the electrical resistance of the wire and the current flowing through it ($I^2R$ loss).

For a DC electromagnet running steadily, this heat is the only power it consumes (apart from power needed to turn it on or off). Large electromagnets can get very hot and often need special cooling systems, like circulating water through tubes integrated into the windings, to avoid overheating and damaging the insulation.

You want to achieve a certain MMF ($NI$) for a desired field. You can get the same $NI$ by having lots of turns and low current, or fewer turns and high current. The power loss is $P = I^2 R$. The resistance $R$ depends on the wire’s material, length, and cross-sectional area. More turns mean longer wire, so $R$ increases roughly linearly with $N$.

If you double $N$ and halve $I$ to keep $NI$ the same, the current $I$ is halved, so $I^2$ is quartered. The resistance $R$ is roughly doubled (since $N$ is doubled). The new power loss is $(I/2)^2 \cdot (2R) = (I^2/4) \cdot (2R) = I^2 R / 2$. You’ve halved the power loss!

So, using more turns and less current for the same MMF is more efficient in terms of heat. Also, using thicker wire reduces $R$ directly for the same length, reducing $I^2 R$.

The catch is that more turns or thicker wire mean the coil takes up more space. If the area available for the winding is limited, you might have to use thinner wire to fit more turns, which increases $R$ and cancels out some or all of the benefit. So, for any given space constraint and desired field strength, there’s a practical limit to how low you can get the heat loss. This minimum heat loss increases with the square of the magnetic field strength ($B^2$).

Inductive Voltage Spikes#

An electromagnet coil is also an inductor.

Inductance is the property of a coil that resists changes in the electric current flowing through it. When the current changes, the inductor generates a voltage (called back EMF) that opposes the change. The voltage is proportional to the rate of change of current ($V = L \cdot dI/dt$).

When you turn an electromagnet on, the current builds up slowly because of this inductance. The power supply has to put energy into the magnetic field being created around the coil.

The bigger issue comes when you try to turn it off suddenly. If you just open a switch, the energy stored in the magnetic field has nowhere to go rapidly. The inductance tries to keep the current flowing, creating a very large voltage spike across the switch contacts. This can cause nasty sparks or arcs that damage the switch.

For small magnets, sometimes a capacitor across the switch can absorb some of this energy. More commonly, a flyback diode (also called a freewheeling diode) is used.

A flyback diode is a diode connected across an inductor (like an electromagnet coil) in a way that it normally doesn’t conduct current when the magnet is on. When the power supply is switched off, the voltage across the coil reverses due to the collapsing magnetic field, and the diode becomes forward-biased, providing a path for the current to continue flowing through the coil and the diode until the energy is dissipated as heat in the wire’s resistance. This prevents large voltage spikes.

For large, powerful electromagnets, you can’t just use a simple switch. They’re typically controlled by sophisticated electronic power supplies that ramp the current up and down gradually. This controlled change in current ($dI/dt$ is kept small) prevents huge voltage spikes. It might even take several minutes to fully energize or de-energize a very large magnet.

Lorentz Forces on Windings#

The magnetic field created by the current flowing in the coil also exerts a force on the wires themselves, because the wires are carrying current in a magnetic field. This is due to the Lorentz force.

The Lorentz force is the fundamental force experienced by a charged particle (or a current-carrying wire, which contains moving charges) when it moves through a magnetic field. The force is perpendicular to both the direction of the charge’s motion (or current flow) and the direction of the magnetic field ($F = q\mathbf{v} \times \mathbf{B}$ or for a wire segment, $d\mathbf{F} = I d\boldsymbol{\ell} \times \mathbf{B}$).

In an electromagnet coil, the magnetic field inside the coil is primarily along the coil’s axis. The current flows around the axis. The Lorentz force, being perpendicular to both, pushes radially outwards on the wires, trying to expand the coil. Imagine the magnetic field lines inside the coil acting like stretched rubber bands pushing outwards.

Also, there’s leakage field between adjacent turns of wire outside the main field. This leakage field can cause attractive forces between turns, trying to pull them closer together along the axis of the coil.

These Lorentz forces get much stronger in powerful magnets (they increase with the square of the magnetic field strength, $B^2$). In big electromagnets, these forces are significant and can cause the windings to move, vibrate, or become stressed. The windings must be built very solidly and clamped tightly to prevent this movement, which could otherwise lead to metal fatigue and failure over time. Designs like the Bitter electromagnet (we’ll touch on this next) are specifically engineered to handle these massive forces by using disks instead of wires and clamping them tightly.

Core Losses (in AC Electromagnets)#

Electromagnets used with alternating current (AC), like in transformers, AC motors, and generators, have a magnetic field that is constantly changing direction and strength. This changing field causes energy losses within the magnetic core material. These losses show up as heat. There are two main types:

1. Eddy Currents: A changing magnetic field passing through a conductor induces circulating currents within that conductor (this is based on Faraday’s law of induction). Since the core material (like iron) is conductive, these induced currents, called eddy currents, flow within the core. They follow closed loops perpendicular to the magnetic field. The energy used to drive these currents is then dissipated as heat due to the core’s electrical resistance ($I^2R$ loss again, but this time in the core itself). To minimize this, AC cores aren’t usually a solid block of metal. They are built from thin sheets (called laminations) of steel, stacked together. Each lamination has an insulating coating on its surface. This insulation prevents large eddy currents from flowing across the entire core. Any eddy currents are confined to flowing within each individual lamination, which greatly reduces their size and the resulting heat loss. Using ferrite cores, which are magnetic but electrically non-conductive, is another way to eliminate eddy current losses.

2. Hysteresis Losses: As the magnetic field direction changes in an AC electromagnet, the magnetic domains within the core material have to flip their alignment back and forth repeatedly. It takes energy to do this flipping, especially because the domains resist changing direction (this resistance is related to the material’s coercivity). This energy is lost as heat. The amount of energy lost per cycle of the AC is related to the area of the material’s hysteresis loop (the graph of B vs. H for the material). To minimize these losses, cores for AC applications are made from “soft” magnetic materials, meaning they have low coercivity and narrow hysteresis loops. Materials like silicon steel or soft ferrites are common choices.

Both eddy current and hysteresis losses increase with the frequency of the AC current.

Superconducting Electromagnets#

To get fields higher than the saturation limit of iron, you can’t rely on the core material boosting the field. You need to generate the strong field purely from the current in the coils. This requires very high currents. However, high currents in ordinary wires create immense heat ($I^2R$).

Superconducting electromagnets use wire windings made of special materials called superconductors. These materials, when cooled to extremely low temperatures (usually with liquid helium), lose all of their electrical resistance.

Since there’s no resistance, enormous currents can flow through the windings without any $I^2R$ heating. This allows them to generate incredibly strong magnetic fields, much higher than iron-core magnets. Superconducting magnets are limited by the point where the high magnetic field itself causes the superconducting material to lose its superconductivity (the “critical field”). As of recent years, they can reach continuous fields in the range of 10-20 T, with record fields pushing past 30 T.

These magnets require expensive and complex refrigeration systems (cryostats) to keep them cold. However, once they are cooled and energized, they don’t consume power to maintain the field (only for the cooling system), which can save energy in long-term operation compared to very powerful resistive magnets. They are essential for things like MRI machines and large particle accelerators.

Bitter Electromagnets#

What if you need a very strong continuous magnetic field, but maybe not quite as high as superconducting magnets can reach, or you don’t need the complexity of cryogenics? For fields stronger than iron saturation but less than typical superconducting limits, or for research flexibility, specially designed resistive magnets are used.

Bitter electromagnets are a type of high-field, water-cooled resistive electromagnet. Invented by Francis Bitter, they don’t use conventional wire windings. Instead, the coil is made from a stack of conducting disks (often copper), arranged in a way that the current flows in a helical path from one end of the stack to the other. Each disk has holes drilled through it.

This disk design is extremely robust and can withstand the immense Lorentz forces that try to tear the magnet apart at high fields ($F \propto B^2$). The holes in the disks allow cooling water to flow directly through the stack, carrying away the tremendous amount of heat generated by the very high current flowing through the resistive copper disks ($I^2R$ heat).

Bitter magnets are used to generate some of the strongest continuous magnetic fields on Earth. As of 2017, a Bitter magnet alone held the record for the strongest continuous resistive field at 41.5 T. Hybrid magnets, combining a Bitter magnet inside a superconducting magnet, can achieve even higher continuous fields, like the 45 T record, by letting the superconducting magnet provide a base field and the Bitter magnet add the extra boost in the center.

The main challenge for both Bitter and superconducting magnets pushing the limits is managing the forces and the heat (or maintaining the cold).

Pulsed High-Field Magnets#

Sometimes, you only need a super-high magnetic field for a very short time. If you pulse a huge current through a resistive coil for just milliseconds or microseconds, you can generate fields much stronger than continuous magnets can handle, even if the coil gets incredibly hot during the pulse. The heat generated during the brief pulse can then be dissipated over a longer time before the next pulse. Using this method, fields up to 100 T have been achieved in non-destructive ways.

The Extreme: Explosively Pumped Fields#

For physics experiments needing truly astronomical magnetic fields, but only for a fleeting moment, there’s a method that uses explosives!

Explosively pumped flux compression generators are devices that create the strongest man-made magnetic fields by using an explosion to rapidly compress the magnetic field produced by an electromagnet.

Essentially, you start with a moderate magnetic field from an electromagnet inside a conductive cylinder. Then, an explosion is triggered to collapse the cylinder inwards. As the cylinder shrinks, the magnetic field lines trapped inside are squeezed into a smaller area. This compression dramatically intensifies the magnetic field for a few microseconds, reaching values around 1000 T. These are often called “destructive pulsed electromagnets” because the device is usually destroyed in the process. While it sounds dramatic, shaped charges are used to direct the main force of the blast outwards, minimizing damage to the surrounding experiment area. They are used for specialized research on materials under extreme conditions.