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# The electric motor

Montreal Web Agency / leeroy

## The electric motor

The discovery of the relation between electricity & magnetism directly lead to the invention of the electric motor. We explain how an electric motor works.

When you place a charged particle in an electric field, it feels a force and starts moving. We explain this observation by saying that the charged particle has an electric field of its own, which interacts with the applied electric field, the result of which is the application of a force on the charge. Likewise, if you place a wire through which a current flows, in a magnetic field, and you observe that the wire feels a force, you’d analogously conclude that the wire has a magnetic field of its own, which interacts with the applied magnetic field, leading to a force being applied on the wire. Although one might argue that the reasoning involved here is faulty – if something is true for electric fields, the same needn’t be true for magnetic fields as well – what we’ve stated here, is fact. Through this article we will be making use of these fundamental concepts to see how an electric motor works.

Michael Faraday and Joseph Henry, in the early 1830s, worked extensively on electricity and magnetism $then thought to be disparate$ and chanced upon an interesting phenomenon. Faraday suspended a wire in a vessel half filled with mercury, and connected the other end of the wire and the bottom of the vessel, to a battery. Mercury being a good conductor of electricity, current flows through the closed path. If however a bar magnet is fixed in the vessel, half immersed in the mercury, the suspended wire does something strange -it starts rotating around the magnet.

Schematic of Faraday’s homopolar electric motor from the early 1800s.

Faraday’s reasoning, as would be later tested several times and eventually confirmed, was that the current carrying wire produces a magnetic field of its own, which interacts with the magnetic field of the bar magnet, hence applying force on the wire and causing it to rotate. This was the first electric motor ever, capable of converting the energy of interaction between electricity and magnetism, into mechanical work.

# Preparing the experiment

Our aim now is to understand the basic principle of working of the Faraday’s mercury bath experiment, and hence learn how a modern electric motor works. Firstly, let us get rid of the practical limitations that may get in our way of understanding the concept in this section. In describing, we will need a wire through which a current flows, which will be placed in a magnetic field. As you know, current flows only when there’s a closed loop $connected to a battery, say$. So, should we consider the entire loop of the wire? No. We assume that the wire does form a closed loop so that current may flow through it, but we observe only a part of this wire, which we indicate in the images, below. Also, there’s no need to question the source of the $uniform$ magnetic field we use. For imagination’s sake, you could assume the field is generated by magnets $which won’t be shown in the images$.

Now, switch on the magnetic field and place the wire in it. Let the wire be placed so that the direction of current flow through it is parallel to the direction of the magnetic field. You will observe nothing. No forces act on the wire. Next, place the wire so that the direction of the current is perpendicular to the direction of the magnetic field. Now you’ll see that the wire segment bends outwards $coming out of the screen$, as can be seen in the image below. Therefore, we may conclude that when the current and the magnetic field are perpendicular to each other, the current wire experiences a force which is perpendicular to both the current and the field $for further reasoning along this line, read this$.

# Fleming’s left hand rule

To ascertain the correct relative directions of the force and fields, John Ambrose Fleming came up with an interesting rule. The rules only work if the two known quantities are perpendicular to each other. The third will then be perpendicular to them both.

Start by stretching out your thumb, forefinger and middle finger, of your left hand, so that they are all perpendicular to each other, somewhat like the x, y, z axes of a coördinate system. Position your hand so that your forefinger points in the direction of the magnetic field, and your middle finger in the direction of the current flow through the wire. Then the direction in which your thumb points, then, gives the direction in which the wire experiences a force.

Force on currents

There’s a right hand rule of Fleming, as well, which concerns with finding the direction of the current produced due to motion of a conductor in a magnetic field – a process reverse to what we’re interested in here. We’ll describe this when we explain electromagnetic induction.

# The electric motor $finally$

Now that we know the rules of the game, let’s lay out the arena. How can we use the force that current wires experience in magnetic fields, and turn it into something very useful? We have seen that in a given magnetic field, current flowing one way, leads to a force on the wire in one direction, while current flowing the other way, causes a force on the wire in the opposite direction. So, the question is, can these opposite forces be used to produce a rotation? We already know that two forces acting on different parts of an object, in opposite directions, will rotate the object. It turns out, there’s a very simple set up that will allow us to produce continuous rotations just making use of the force the current wires experience in magnetic fields.

As we pointed out in the beginning, current flow requires a closed loop. Therefore, we consider a loop of a conducting wire in a shape as shown in the image below. We have an almost-rectangular loop , whose ends are connected to a battery. The battery is the source of the electric current through the loop. On either side of the rectangular loop, we place magnets of opposite polarities. These magnets will be responsible for the required magnetic field.

Now, with the current loop immersed in the magnetic field, we analyze if there are any forces experienced by the loop due to the field. Let’s pick the part AB of the loop first. We observe that the current flowing through this segment of the wire is perpendicular to the direction of the magnetic field due to the magnets. Hence, we may apply the Fleming’s left hand rule, to find the direction of the force on the wire segment. $We hope you have your left hand fingers stretched and ready, right now.$ With the magnetic field going rightwards, and the current flowing from A to B, we find that the rule tells us that the direction of the force on the wire AB is “downwards”. Next, pick the segment CD of the loop. Here, the direction of the current is opposite to that in AB, while the magnetic field is unaltered in any way. So, naturally, the rule tells us that the force on the segment CD is “upwards”. And what about the segments BC and DA? They are always parallel to the magnetic field direction, and hence, experience no force at all, from the magnetic field.

Schematic diagram of an electric motor $commutator and brushes magnified$.

In conclusion, there’s a downward force on the segment AB and an upward force on the segment CD, of the rectangular loop. These two forces will cause the entire loop to start rotating $counter-clockwise, as seen from the perspective of the image above$. Now, consider the situation when the loop has rotated by 90 degrees. The force on the segment CD will continue to point upwards, while the force on AB will remain downwards. In this configuration, the two opposite forces won’t cause a rotation, but will conspire to change the shape of the loop $which we won’t allow to happen, by taking care that the material of the wire loop is strong enough to withstand the distorting force$. Despite there being no forces to cause further rotation, the loop continues rotating due to inertia. Once the loop has rotated through 180 degrees, apply Fleming’s left hand rule. You will find that the force on CD is still upwards, while the force on AB is still downwards $AB and CD have exchanged places, with the direction of current flow through each, unaltered$. Which means, that the forces now will cause a rotation in the opposite direction, bringing the loop back to where we started. And the process repeats over and over again – the loop oscillates.

# Getting it to rotate continually

A back and forth oscillation isn’t of much good use. What we need is a continuous rotational motion. To make this happen, we first realize that the core reason for the oscillatory motion of the loop is that the direction of current through each segment of the loop remains the same all through the motion. If we had a mechanism to somehow flip the direction of the current through each segment of the loop, every “half rotation”, we could have a continuous rotatory motion. We accomplish this task by using what is called a commutator.

The commutator is basically a ring split into two, which is fixed in place, and to which are connected two conducting brushes as shown in the image. The brushes are connected to the battery terminals, while the rings are connected to the ends of the rotating loop ABCD. With this set up, as the loop rotates through every 180 degrees, the direction of the current through the loop flips. And hence we have a perpetual rotational motion, caused solely due to the force current-carrying wires experience when placed in a magnetic field.

What started with accidental discoveries of the connection between electricity & magnetism, has quite cleverly been converted into something of immense use for us. For there isn’t $and can never be$ any dispute regarding the wonders an electric motor is capable of.

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Roshan Sawhil is a Physics postgraduate who rejoices both doing and explaining Physics. He also finds doing Philosophy as a leisure activity quite interesting. You can find and connect with him on Facebook and Twitter.

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