Physics · Electricity and magnetism · Grade 8

Electromagnet and relay

How does a crane lift a tonne of iron, and why does it drop it when the current is cut?

The situation

At a scrap-metal yard a huge steel disc hangs from a crane hook. When the operator presses a button, the disc “sticks” an old car body to itself and carries it over to a railway wagon; when the current is cut, the body drops. This is an electromagnet: a coil wound on an iron core. The same device works in a doorbell, inside a relay, and in a nail in the school laboratory. What does the force of an electromagnet depend on, and how is it controlled?

Topic

Electromagnets and relays. Electromagnet on a scrapyard crane, a doorbell and a relay

Key ideas

Electromagnet
Lifting force
Electromagnetic relay

Formulas

B = \frac{μ_{0} μ N I}{l}

The field inside a long coil with an iron core is proportional to the number of turns $N$ and the current $I$ (until the core saturates).

F = \frac{B^{2} S}{2 μ_{0}}

The lifting force of a pole face is proportional to the square of the flux density.

N I = Φ R_{m}, R_{m} = \sum_{k} \frac{l_{k}}{μ_{0} μ_{k} S_{k}}

“Ohm's law” for a magnetic circuit (Hopkinson's law): magnetic flux = magnetomotive force / reluctance.

R_{m}^{a i r} = \frac{2 δ}{μ_{0} S} ≫ R_{m}^{i r o n} = \frac{l}{μ_{0} μ S}

An air gap of a few millimetres gives a greater reluctance than metres of iron.

P_{c t r l} = U I ≪ P_{l o a d}

Relay: a weak control circuit (mA) switches on a powerful circuit (A).

Theory

What is an electromagnet?

A coil carrying current becomes a magnet; if an iron core is put inside, the iron becomes magnetised and the field grows hundreds to thousands of times stronger ( $μ ≫ 1$ ). The difference from a permanent magnet: an electromagnet can be controlled by current — switched on and off, its strength changed, its poles swapped by reversing the current. In the laboratory mode, take out the core: the number of clips falls to zero.

Lifting force and saturation

The pulling force of a pole face is $F = B^{2} S / (2 μ_{0})$ . At small currents $B \propto N I$ , so $F \propto {(N I)}^{2}$ : double the current and the force grows four times. But the magnetisation of iron is limited — saturation ( $B \approx 1.7$ – $2$ T): in the crane mode the $F (I)$ graph flattens at the top. The force is very sensitive to the gap: rust, paint or an uneven surface reduces the force sharply — which is why a flat steel plate is lifted much more easily than a car body.

Magnetic circuit

The magnetic flux $Φ$ “flows” along a closed path like an electric current: in a crane magnet, from the central pole through the load to the outer ring and back. The magnetomotive force $N I$ is divided by the reluctance of the circuit, $R_{m} = \sum l / (μ_{0} μ S)$ . In iron $μ$ is large — the reluctance is small; in an air gap $μ = 1$ — the reluctance is enormous. That is why an electromagnet is strong when it touches the load, and several times weaker when it is 5 cm away. Switch on “Magnetic circuit” to see the path of the flux.

Electromagnetic relay

A relay is an electromagnetic switch. A weak control circuit (12 V, a few tens of mA) magnetises the coil, the armature is pulled in, and the contacts close a powerful circuit (230 V, a few amperes). The two circuits are electrically isolated — this is safe. The relay closes at the pull-in current, but once it has closed the gap shrinks and a much smaller current is enough to hold it: reduce the voltage and find the release voltage. Relays have been and are used in car starters, lifts, traffic lights and the telegraph.

The electric bell — a self-interrupting circuit

When the button is pressed, current goes through the contact screw to the coil, the armature is pulled in and the hammer strikes the gong. But as soon as the armature moves, the contact breaks — the current stops, the spring returns the armature, the contact closes again and everything repeats (tens of times a second). The frequency depends on the stiffness of the spring, the mass of the armature and the voltage; at a very low voltage the pull cannot overcome the spring. The small spark that flashes when the contact breaks is the result of self-induction (in the “Self-induction” experiment).

Lab: the simplest electromagnet

Aim: to study how the force of an electromagnet depends on the current and the number of turns. Insulated wire is wound on a nail, and a battery, a rheostat and an ammeter are connected in series. Dip the end of the nail into paper clips, lift it and count how many clips are hanging on. Make a table, changing the current $I$ (the number of turns constant), then changing $N$ (the current constant). Conclusion: the force increases quickly as $N I$ increases, and a coil without a core lifts almost nothing. Model: the field at the end of the nail is $B \approx \frac{1}{2} μ_{0} (H + M)$ , $H = N I / l$ , and the magnetisation of a thin rod is limited by its own demagnetising field ( $M \approx H / N_{d}$ , $N_{d} \approx 0.007$ ).

Did you know?

The first electromagnet was made in 1824–1825 by the English inventor William Sturgeon: a horseshoe of iron with wire wound on it, weighing about 200 g, which lifted a load of about 4 kg on the current of a single galvanic cell.
In 1831 the American physicist Joseph Henry built an electromagnet for Yale University: with an iron core of about 27 kg, it held a load of 936 kg (2063 lb).

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Circuits and Kirchhoff's rules — Grade 8
Electric current in metals — Grade 8
Electrolysis, Faraday's laws — Grade 8
Electric current in vacuum and gases — Grade 8
Magnetic field — Grade 8
Shake torch — Grade 10
Self-induction — Grade 10
Magnetic properties of matter — Grade 10
Plasma — the fourth state — Grade 10
Power transmission line — Grade 11