 Here you see a metal plate, for example made of copper. If you apply a voltage between the two ends of the plate, then negatively charged electrons move from right to left through the plate to the positive pole. First, nothing happens. The electrons simply flow straight to the positive pole. But if you now put the metal into a homogeneous magnetic field B, whose field lines penetrate the metal, then a magnetic force acts on the moving electrons and deflects them upwards. This magnetic force is called Lorentz force. Let us denote it by fm. Why upwards? Because in this case the magnetic field B points into the screen and the left-hand rule yields the direction upwards. In the magnetic field, electrons therefore no longer flow on a straight path to the positive pole but accumulate in the upper part of the metal plate. This results in an excess of electrons in the upper part of the plate and a deficiency of electrons at the bottom. An approximately homogeneous electric field is formed between the two ends of the metal as if the two ends were two capacitor plates. While the other electrons traveling through the metal now experience not only the magnetic force but also an electric force. Let us denote it by fe. The electric force points downward because negatively charged electrons are repelled downward by the electrons at the top of the metal. Thus, the electric force on an electron acts exactly opposite to the magnetic force. If the magnetic force is greater than the electric force, the electron moves upwards. This deflection of electrons happens until an equilibrium of forces is established. This generated charge difference, which no longer changes, corresponds to a constant hull voltage. We denote it by uh. If you were to measure the voltage between the upper and lower end of the metal with a voltmeter, you would measure the value of the hull voltage. How can we calculate hull voltage mathematically? Let's quickly derive a formula for hull voltage. The formula for the Lorentz force is q times v times b, q is the charge of the particle in the magnetic field, in this case the elementary charge of the electron, v is the velocity of the electron and b is the strength of the applied external magnetic field. The formula for the electric force on the electron is q times e, e is the strength of the homogeneous electric field between the upper and lower end of the metal. Set the two forces equal. Electric charge cancels out. The e field prevailing in the metal is not directly known, but there is no problem because we can measure the hull voltage instead and divide it by the width h of the plate. Also replace the e field in the formula with u divided by h. Prearrange the equation for the hull voltage, u is equal to h times v times b. You can't measure the velocity v of the electrons directly, therefore we replace it with the length l of the metal plate divided by the time t, which the electron needs to traverse the distance l. Replace v with l divided by t. Now we have eliminated v, but thereby brought the unknown time t into play. With an emmeter you can measure the current i that flows from the right to the left end of the metal plate. The current i is defined as the amount of charge big q per time t. Rearrange for t. The amount of charge big q is the number n of electrons times the charge small q of each electron. Now substitute unknown time t with n times q divided by i. But how do you know how many electrons travel through the metal plate per time? For this we use the charge carrier density small n. It is defined as the number n of charges per volume v of the metal. Rearrange it for big n and then eliminate big n by using small n times v. The volume of the plate is the length l times width h times thickness d. L and h cancel each other out so that only the thickness d of the plate remains in the formula. The factor 1 divided by n times q is called the Hall constant and is abbreviated as ah. The Hall constant depends on the used metal and can be determined in an experiment because you can easily measure the current i, thickness d and magnetic field b.