In the previous article, we had obtained an important formula for cathode rays, as we see them now, with three unknown parameters of cathode ray particles: charge, mass, and velocity square.
Three unknown parameters, one equation can not be solved, so we need at least one equation, so what to do? That's what we are today, and in addition to being able to apply an electric field to cathode rays, we can also apply a magnetic field.
So before talking about the magnetic deflection of cathode rays, let's briefly understand the history of human research on magnetic phenomena. Let's get down to business.
Magnetic phenomenon was actually found earlier than the electrical phenomenon, which is the earliest discovery of our Chinese, and it is also the first to use the characteristics of magnets to point north, making the earliest compass, but we did not use it to navigate, but looked at feng shui, which is a pity.
In the West, the study of magnetic phenomena is relatively late, and around the 13th century, Westerners noticed that natural magnets have two poles, one refers to the northern end and the other is the guide end.
But Westerners soon applied this phenomenon to navigation, and in Elizabethan times, the court physician who studied the phenomenon of electricity, William Gilbert, guessed how the compass worked based on the homopolar repulsive and heteropolar properties of the magnet.
The compass can refer to the north because the earth itself is a large magnet, and the geographical north pole of the earth is the magnetic south pole, which attracts the magnetic north pole on the compass.
Since Gilbert was also studying electrical phenomena, he found that electricity and magnetism have some similarities, such as attraction and repulsion, but there are still many differences between electricity and magnetism.
For example, magnets do not need friction to attract iron, but can not attract other objects, and the electricity generated by friction can attract debris of any substance.
So Gilbert did not find a correlation between electromagnetism. It was not until the 19th century that the Frenchman Christian Oster discovered the phenomenon of electromagnetism.
It is said that in 1820, he found a slight oscillation of the compass pointer next to the energized wire, and after repeating several experiments, this phenomenon still occurred, and in July of the same year, he found a battery with a stronger voltage and repeated the experiment.
Found that the compass pointer after a violent swing, and finally the pointer in the direction of the vertical and wire stabilized, if you continue to move the compass along the direction of the pointer, you will find that there is an invisible force around the wire around the wire, we now know that this is the magnetic field generated by the energized wire, the magnetic field direction can be judged according to the right hand rule, then change the direction of the current, the direction of the magnetic field will be reversed.
On September 11 of the same year, Amper found on the basis of Oster's research that there is no need for magnets, and that two parallel energized wires will also produce a force between them, and if the current direction is the same, they will attract each other, and the opposite will repel each other. Therefore, Ampere concluded that the essence of magnetic phenomena is actually an electrical phenomenon, or a phenomenon of electrical magnetism, so the reason why natural magnets are magnetic must be because there is an electric current inside.
At that time, amperes certainly did not know how the magnetism of matter was produced, but he also said that it was not bad, and now we know that this is because the outermost layer of the atom does not have the spin of paired electrons, and the net residual magnetic moment is generated, if these atoms are arranged in the same direction, then the whole object will show magnetism.
Ampere's discovery is the initial unification of electromagnetic phenomena, then the person who finally completed the unification of electricity and magnetism is maxwell, who told us through a set of equations reflecting the symmetry of the field, in fact, different manifestations of the electromagnetic field. The electromagnetic field is the electric and magnetic field that oscillates vertically in space, and now we know that light is also an electromagnetic field, and the smallest electromagnetic field is a light quantum.
Ampere then also gives the formula for the force between two energized wires, the force of wire 1 on wire 2 = 2Km× the current in wire 1 × the current in wire 2 × the length of the wire / (the distance between the two wires).
Where Km is a constant, when the unit of force is Newtonian and the unit of current is amperes, km is measured at 10^-7. If we look at this formula, we will find that the force on wire 2 in wire 1 is always proportional to its own current and its own wire length.
So we can follow the method of prescribing the electric field, here to introduce the concept of magnetic field, we can take the formula of 2Km× the current in wire 1 / (the distance between the two wires), as a whole, which is the strength of the magnetic field generated by the current in wire 1.
So this formula can be written as follows: the force on the wire = the current in the wire× the length of the wire× the strength of the magnetic field. It can also be seen from this formula that the unit of magnetic field is the force divided by the current divided by the length, so it is cattle / (ann · meter), in fact, there is a more commonly used magnetic field unit called Gauss, defined as 1 gauss is equal to 10 ^-4 niu / (ann · m).
In fact, the force of the wire in the magnetic field is also related to the angle between itself and the magnetic field, and the force is the largest when the angle is 90 degrees, and the force is not affected when it is parallel to the magnetic field. Here we only consider the case where the angle is 90 degrees.
Like the electric field, the magnetic field is also a vector, that is, there is a direction, so we artificially stipulate that at a point in the magnetic field, the direction pointed to the north end of the compass pointer is the direction of the magnetic field. So the magnetic field lines we see around the magnet are drawn like this, coming out of the north pole and pointing to the south pole, and the direction of the magnetic field generated by the energized wire can be judged according to the right-hand spiral rule. When charged particles move in a magnetic field, the direction of the force can be judged according to the left-hand rule.
The magnetic field strength here is also easier to calculate, if the current of an energized wire is 10 amperes, then the magnetic field strength at 0.01 meters from the wire is 2×10^-7×10/0.01=2× 10^-4 N/ampere, and the strength of the geomagnetic field is about 5× 10^-5 N/ampere, so the energized wire can deflect the compass pointer.
The biggest application of this phenomenon is the telegraph, we can use the compass pointer to judge the opening and closing of the entire circuit, which is a way to transmit signals, so the telegram we see on the TV is constantly pressing the switch. However, the length and spacing of the switches were compiled into telegrams.
With the above knowledge, we will now say that the cathode rays are deflected under the magnetic field, in Thomson's experiment, he applied a uniform magnetic field to the cathode rays, but just now we are talking about the current in the energized wire in the magnetic field, and now we have to know the force of the individual particles of the cathode rays in the magnetic field, so the formula has to be changed.
Now imagine a wire in which a particle moves, and the length of the wire should be equal to the speed of the particle multiplied by the time it has been moving in the wire.
Therefore, in the formula of magnetic field force, the length of the wire × current = the speed of the charged particles× the time it takes for the charged particles to pass through this wire × the current, because the definition of the current is the amount of charge passed through per unit time, so the time it takes for the charged particles to pass through this wire × current = the total amount of charge in the wire.
Therefore, the length of the wire × current = the speed of the charged particles × the total charge in the wire, so the original formula for the magnetic field force becomes the force received by the energized wire = the speed of the charged particles× the total charge in the wire × the magnetic field strength.
Since the charge and velocity of each charged particle in the wire are the same, they divide the current in the wire equally into the force received in the magnetic field, so the force received by a single charged particle perpendicular to the magnetic field movement = the speed of the charged particle × the charge of the charged particle × the magnetic field strength.
For example, in the particles of the solar wind, the average charge carried by the particles is 2×10^-19 coulombs, the speed is about 5×10^5 m/ s, just said that the earth's magnetic field strength is about 5×10^-5 N / (ann · m), then according to the above formula, we can calculate that as long as these particles are perpendicular to the earth's magnetic field motion, then it will be subjected to a force of 5×10^-18 niu, this force is super small, but the mass of the particle is even smaller about 5×10^-26 kg. So the Earth's magnetic field will provide a very large acceleration to the particles, about 10^8 m/s. This acceleration is very impressive, so the Earth's magnetic field can effectively block these charged particles for us.
One thing that is particularly interesting is that charged particles are subjected to the greatest force when they move perpendicular to the magnetic field, but they are not subject to force parallel to the magnetic field movement, so in the end the solar wind particles enter the earth from the poles of the earth along the earth's magnetic field line, so the aurora can only be seen at the poles.
Now we substitute the formula for the force of the charged particle in the magnetic field into the equation for the displacement of cathode rays under the action of the force, and we can know: deflection caused by the magnetic field = the charge of the ray particle × the strength of the magnetic field× the distance of the deflection zone× the distance of the drift zone / (the mass of the ray particle × the speed of the ray particle)
In this formula, the magnetic field strength, the distance of the deflection region, and the distance of the drift region are all known, so we can calculate: the charge of the ray particle / (the mass of the ray particle × the speed of the ray particle) = the deflection displacement caused by the magnetic field.
In the previous lesson, we also obtained a formula by applying an electric field: the charge of a ray particle / (the mass of the ray particle × the velocity of the ray particle ^2) = the deflection displacement caused by the electric field.
Now we are one step closer to success, and many terms are the same in these two formulas, so we can go to the ratio of the two and we can get: magnetic deflection displacement / electrodeflection displacement = (magnetic field strength / electric field strength) the velocity of × ray particles.
Since the deflection displacement and the magnetic field strength and electric field intensity are known, we calculate the velocity of the ray particle, and then we substitute the speed into the electric deflection or magnetic deflection formula, and we can calculate the charge-mass ratio of the cathode ray particle.
This was the main process by which Thomson won the Nobel Prize. Now let's look at the experimental data measured by Thomson at that time, in fact, Thomson did many sets of experiments, using different cathode materials, using different electric field intensities and magnetic field strengths, and the length of the deflection zone of the cathode ray tube he used was 0.05 meters, and the length of the drift zone was 1.1 meters.
The set of data we see now is the result of Thomson's measurement at that time, and the last column is the mass-to-charge ratio of cathode rays, the average value is 1.3× 10^-11 kg/coulomb, it can be seen that the results obtained in various cases are basically the same, so Thomson came to the conclusion that cathode rays are negatively charged particles, which have a definite charge-to-mass ratio, and have no relationship with cathode materials. So Thomson believed that cathode ray particles were the basic materials that make up all the atoms of matter.
Finally, let's say that the mass-to-charge ratio of electrons measured today is actually twice as small as Thomson's, which is 0.56857× 10^-11 kg/coulomb.
It can be seen that Thomson's measurement results that year were a little far away, and it did not give the margin of error for each measurement, if Thomson handed out this paper today, it would definitely be returned, and the Nobel Prize would not be thought of.
But this is more than 100 years ago, and everyone knows that Thomson's hands are stupid and not good at experimenting, but his methods of experimenting with electrical and magnetic deflection are no problem. Now we estimate that Thomson was conducting an electrical deflection experiment, and there was a systematic error in the measurement of the strength of the electric field between the charged metal plates, so it led to a highly consistent experimental result, which is actually relatively lucky.
However, Thomson also used other methods to obtain a more accurate mass-to-charge ratio, in which Thomson collected cathode rays into a metal container, which can collect the charge and kinetic energy of cathode rays, and the kinetic energy will be converted into heat, so that the temperature of the metal container will increase. By measuring the temperature, it is possible to know how much heat is collected by the metal container.
Then the ratio of accumulated heat to accumulated charge is the ratio of kinetic energy and charge of each shot particle, then the formula is written like this, the accumulated heat energy / accumulated charge = 1/2× the mass of the particle × velocity² / the charge of the particle.
Replace the formula for electrical deflection with this formula, and we can also calculate the velocity and mass-to-charge ratio of cathode ray particles based on this formula and the formula of magnetic deflection.
The figure above is the parameters of the cathode rays measured by Thomson through the conservation of energy relationship, and it can be seen that Thomson used three sets of cathode ray tubes, and the experimental results of the first two groups were similar to today's values, but Thomson did choose the third set of experimental results, and the values cited in his future articles were 10^-11 kg/coulomb.
Because this result is relatively close to the result of the first measurement, Thomson chose this value. But in any case, in an era when it was uncertain that atoms did not even exist, Thomson's experiments made those who insisted on atomism determine that there was a more fundamental particle in the atom.
Although Thomson did not give the negatively charged particle a name, he firmly believed that the components of the atom had been found, which were negatively charged and should have a small mass, so Thomson was the first to discover the electron.
Well, that's it for today, and in the next lesson we'll talk about how humans measure the mass and size of atoms.