Have you heard of the right hand rule? Surely, if you don’t know it, the first thing that has come to mind when you hear about right-handers has been something related to cycling. When we ride a bicycle on the road, there is a code that we must follow to alert cars and other vehicles on the road of our intentions. While cars and motorcycles can benefit from electronic signals in their vehicles that allow a light to alert them to their intentions, bicycles do not have this advantage. For this reason, the direction that is going to be taken in case it is going to be rotated is usually indicated with the hand as the rotation movement that the Earth makes throughout a day.
However, when we talk about the right-hand rule, we mean something totally different and that has nothing to do with road traffic. It is related to the scientific field, and more specifically to the electromagnetic field, with a clearly oriented use of vector products. Without a doubt, something totally multidisciplinary.
What is the right hand rule?
Focusing now on the field in which we refer to the right-hand rule, we are going to define it as a methodology that is basically used to determine the direction of different vectors, based on planes typical of cartography. For those who do not know, cartography is the science that studies maps and the possibilities of orientation in space. Historically, they referred especially to ships and the ways in which they were oriented when they sailed, with special emphasis on the colonial era when constant movements were made from the New World to the European continent. With this rule, centered on the use of a screw or even a corkscrew, this vector advances when we turn it to the right, that is, clockwise. On the other hand, when we do it in the opposite direction, that is, in an anti-clockwise direction, it goes back. A similar rule for electrical engineering students is impedance.
Therefore, taking this description into consideration, the formula that would allow us to determine a vector that we will call C will be the direction we take starting with another vector that we will know as A, and following another that we will name B. The most used examples of this right-hand rule are found, as we have mentioned before, in all fields related to something electromagnetic. Thus, if the thumb of the vector rotates to the right, the electric force in the magnetic field will advance, while if it rotates to the left, it will recede. Let’s think about something more everyday, such as opening a bottle of wine. In general, these usually have a cork stopper. We will require a kind of vector. If we want this vector to advance penetrating the cork, we will move it in a right direction. On the other hand, if, on the contrary, we want it to go back, it will be enough to turn it to the left.
If we go back to the electromagnetic field, we will be able to find a second really interesting possible application. We take the right hand as a reference. When the thumb of the latter is placed upwards, it marks, as we have said, the direction of the vector itself. However, if the rest of the fingers are pointing towards the palm of the hand, we will be clearly describing what is known as a rotation movement. At the same time, the direction of both the thumb and the rest of the fingers will serve to mark whether the direction of rotation of the vector is clockwise, or instead, it does so in an anterior clockwise direction. Another of the peculiarities of this rule of the right hand is the finger that is used, since depending on this, it will have a totally different use or another. For example, the thumb, as we’ve mentioned above, is mostly used for all things force-related. On the other hand, if we use the index we will be in the speed field. Finally, the central finger, also known as the middle finger, would enter the electromagnetic fields. Another of the varieties of this rule is obtaining both the direction as of movement of a given force within an electromagnetic field.
At a mathematical level, the so-called Lorentz Law is followed. In this formula, the force, also known as vector product, is obtained from the product of the charge times the velocity and later the magnetic field. If we represented it on a graph, the line of force would be totally perpendicular to that of velocity and that of the electromagnetic field. Next, with the index and the heart will be the fingers with which we mark the strength of the vector product. Whenever the thumb has an upward direction, said force will be positive while otherwise, if we have it downwards, the force will be completely negative. Obviously, if we are familiar with mathematics it will be really difficult to understand what uses can be given to the right-hand rule. In addition, it also requires some prior knowledge in the world of physics to be able to understand it. However, later we will try to clarify it with an example so that everything is much clearer and there is no doubt.
Benefits of the right hand rule
All in all, the right-hand rule has numerous uses in the field of physics and mathematics, giving its knowledge numerous benefits that are worth knowing. The most prominent are the following:
- General culture. As they say, knowledge does not take up space. In this sense, although our field is a totally different one, it never hurts to know the right hand rule for future uses that we can give it.
- Develop a professional career in the field of mathematics. If we want to dedicate ourselves to a profession related to the field of physics or mathematics, obviously it will be necessary to know the right hand rule because it can be really useful for us.
- Creation of electromagnetic fields. Magnetic fields have enormous peculiarities. In this sense, in order to master them it will be necessary to have a really extensive knowledge about them. This theory can help us develop such knowledge.
- Scientific investigation. This type of theories have contributed throughout history to develop different types of research, and to the proliferation of new theories. Therefore, carrying out theories of this type will always be positive for everyone.
How the right hand rule is applied:
The right hand rule has numerous applications, both in the scientific, technological and industrial fields. Since the manufacturing process began, starting with the production line created by Henry Ford, industrial machinery has had many different applications that must be considered. Currently, numerous machines and different processes follow the right-hand rule. The way they move, the direction, the force and the orientation in the movements of rotation and translation follow exactly the principles of this theory. Even in some fields of robotics, some of the practical principles are also carried out. Let’s not forget that we live more and more in a society dominated by automation and by ensuring that those processes that previously required human intervention are now totally autonomous. In this sense, something that belongs to the nano age can use a priori principles as primary as this type of theory could be.
Let’s go with a practical case. Let’s say we have a type of electrical conduit made of copper that forms a coil. If we give it electric current of low or moderate intensity, we will be able to generate an electromagnetic field that will be totally perpendicular to how the different electrons move within the coil itself. This would be the right hand rule. However, we can find even more examples like this one. Now we start from the base that we have a piece of iron that makes a U shape. In this piece, we also have another small block of iron that fits inside the big piece. If we give it current with a U-shaped coil, we will be able to create an electromagnetic field that will be totally perpendicular as indicated by the right-hand rule. On the other hand, when we stop applying said current, the electromagnetic field will disappear and, therefore, said theory will no longer be fulfilled.
The applications of the right hand rule, as we indicated previously, can be really varied in the industrial sector, such as car alternator repair. Obtaining a vector product will be the most common use that we can give it. In this case, basically when a point A rotates towards another B, a product C will be obtained by generating a rotation movement. Following the same line, let’s also remember that a translation movement can be generated, in addition to obtaining a force within an electromagnetic field. All these three concepts, moreover, can be completely interrelated with each other in a totally practical way. In addition to the direction of that vector A towards B, creating vector C, as a vector product, we can also decipher the speed of the angle of rotation or torsion that we can achieve if we apply the right-hand rule. During the angular turn from the angular speed that we are using, what is known as angular momentum is also produced. This rotation is expressed in kilos per meter/second and it is a new variable totally applicable to the ones that we have already explained before that can allow us to obtain more information.
The direction in which the magnetic field will be directed is another of the main applications of the right-hand rule. Let’s not forget the basics that we have explained above. The direction of the thumb will serve to determine where the electromagnetic current will be directed. When the thumb points to the right, the current will rotate clockwise, while if it points to the left, it will rotate counterclockwise. If we can determine the direction of the magnetic field, we can also determine the force that it is going to exert inside the magnetic field. However, the force is not that of the vector product, but of the magnetic field on the same vector product. Finally, we can also apply it in the orientation of the angle of the axis. When the vector advances from x to y, it will do so by describing a parabola or a straight line that we can call z, and which, we can orient the angle that will describe the force within the electromagnetic field. Undoubtedly, the right-hand rule has meant a great technological advance in the field of physics or mathematics.