 Lawrence force is an electromagnetic force experienced by a charged particle in an electric and magnetic field. If the electric field is zero, and we will assume it here, then the Lawrence force is purely magnetic force acting on a charge as it moves through a magnetic field. The cause of the Lawrence force is a moving charge in the magnetic field. No moving charge or no magnetic field, then there is also no Lawrence force. Let's take a negatively charged electron and send it from left to right through a simple homogeneous magnetic field. The magnetic field points out of the screen here. The Lawrence force points upwards in this case and the moving electron is therefore deflected upwards. If on the other hand the electron moves from right to left in the magnetic field, then it is deflected downward. What happens if we change the magnetic field direction by 180 degrees? Now the magnetic field points into the screen. If the electron now moves from left to right through this magnetic field, it is no longer deflected upwards but downwards. Let's first learn how to determine in which direction the electron is deflected. For this, we use the so-called left-hand rule. The thumb points in the direction of the movement, that is to the right. The index finger points in the direction of the magnetic field, that is into the screen. And the middle finger points downwards in this case, indicating the direction of the Lawrence force. The electron is deflected downwards. If on the other hand the electron moves from right to left, then the direction of movement changes. The thumb now points to the left. The index finger points again into the plane. And the middle finger now points upwards. Lawrence force thus deflects the electron upwards. What if instead of the electron, a positively charged particle, such as a proton, moves from left to right? If a positively charged particle moves through the magnetic field, then we use the right-hand rule. The application of the hand rule remains the same. The thumb points to the right. Index finger into the screen. The middle finger, that is the Lawrence force, points upwards. So we can state that positive charges are deflected exactly in the opposite direction to negative charges. And we use the right-hand rule for positive charges. For negative charges, the left-hand rule. How can we calculate the Lawrence force as a magnetic force? Let us denote the charge of the particle with a letter Q. We denote the Lawrence force with Fm. The velocity of the charge with V and the strength of the magnetic field with B. B is also called magnetic flux density and indicates how strong the magnetic field is. The unit of B is Tesla. In an experiment, we can observe three things. If you double the charge Q, then the Lawrence force on the particle doubles. Mathematically, this relationship means that the Lawrence force F is proportional to the charge Q. If you double the velocity V, then the Lawrence force also doubles. So V is also proportional to the Lawrence force. The same is true for the magnetic field B. If you double the strength of the magnetic field, then the Lawrence force will be twice as large. Other parameters such as the mass of the particle do not affect the magnitude of the Lawrence force. So we can write down a formula for the Lawrence force. F is equal to Q times V times B. If you know the charge Q, the velocity V, and the homogeneous magnetic field B, which is perpendicular to the direction of velocity, then you can calculate the value of the Lawrence force. By the way, Lawrence force has the unit Newton. You don't always have the simple case where the charge flies perfectly perpendicular to the magnetic field direction. Here we see the magnetic field lines from the side. Previously, we had the case where the charge was perfectly flying at a 90 degrees angle through the magnetic field. But if it flies under an angle alpha, which is not 90 degrees, then we have to add sine of alpha to the QVB formula. Remember, if the charge is flying at an angle to the homogeneous magnetic field, then you use this formula. And if the charge flies perpendicular, then alpha is equal to 90 degrees, and the sine of 90 degrees is 1. This results in the original simple QVB formula. We noticed earlier that an electron moving to the right is deflected downward in this magnetic field. But it is not deflected downwards arbitrarily. Let's look at what will happen after the deflection. Let's zoom out. We will see that the Lawrence force always acts at a 90 degree angle to the direction of velocity. This is what nature tells us. This has the consequence that the electron is forced to a circular motion. This resulting circular path has a certain radius r, and this radius depends on how large the Lawrence force on the particle is. A particle which performs a circular motion and has the mass m is held on the circular path by the centripetal force Fz. In this case, the Lawrence force acts as the centripetal force. So set the formula for the Lawrence force equal to the formula for the centripetal force. This QVB is equal to m times V squared divided by r. We can cancel the velocity V one time on both sides. Then we get a formula with which we can determine, for example, the radius r of the circular path. We can easily determine the radius of the circular path, for example, in a Telton tube experiment. It is much more difficult to find out the velocity V of the electron. The derived formula is perfectly suitable for this purpose. We rearrange it for the velocity V. If we measure a radius of 1 cm, that is 0.01 m, and set a magnetic field of 5 mT, we get a speed of 8,791,000 m per second. So the electron moves on a circular path with almost 3% of the speed of light. So that's it. In the next video, we will discuss how Lawrence force acts on current carrying wires. With this in mind, bye and see you next time.