Electricity and magnetism/Electrostatics/Electric voltage

In steady state, the electric voltage is the difference in electric potential between two points. Its unit of measurement is the Volt (V). What is potential? To understand potential, we must understand the work of a force. We can reason about the electric potential in the same way as about the gravitational potential. We can move a heavy object effortlessly on an ice rink, because we don't have to fight against the force of gravity. On the other hand, it takes a lot of effort to lift a heavy object vertically, because we have to oppose the force of gravity. In the first case, the force of gravity does not work, because the movement is horizontal. In the second case, the force of gravity works, because the movement is vertical. The work W of a force f on a mobile moving in a straight line over a length d is equal to the scalar product of the force vector f and the displacement vector d: W = f.d = f d cos where is the angle between the force vector f and the displacement vector d. f and d are the lengths of the vectors f and d. The force of gravity is vertical. It does not work for a horizontal displacement because cos 90° = 0. The work of the force of gravity on a mass that is raised from a height is 240px The work of a force is energy. If > 90°, cos < 0 and W < 0. The work of the force has a negative value because it is the energy lost by a body that moves against the force. This lost energy can be the kinetic energy E = 1/2 mv2. The speed v decreases because the body is slowed down by the force. If < 90°, cos > 0 and W > 0. The work of the force has a positive value because it is the energy acquired by a body that moves by being pushed and accelerated by the force. In the international system of units of measurement (MKSA, meter, kilogram, second, Ampere), the unit of energy is the Joule (J). One Joule is the work required to move a body one meter against a force of one Newton (N). 1 J = 1 N. 1 m = 1 N.m The force of gravity on the surface of the Earth is approximately equal to 9.8 N, almost 10 N. One Joule is therefore approximately the energy required to lift a 1 kg body ten centimeters. When the trajectory of a mobile is a curved line, we calculate the work of a force by reasoning on broken lines which follow the curved trajectory. If the lengths of the segments are shorter and shorter, a broken line becomes more and more similar to the curved line it follows. We find the work of the force by taking the limit of the sum of the work on each segment, when the length of the segments tends to zero. The work of the force is the integral of the scalar product of the force and the displacement vector on the path followed. By definition of the scalar product, the work of the force of gravity g on an inclined segment AB is equal to g(hA - hB) where hA - hB is the altitude difference between its two ends. Now the altitude difference between A and C is equal to the sum of the altitude differences between A and B and between B and C: hA - hC = (hA - hB) + (hB - hC) So the work of the force of gravity g on any path going from A to Z is always equal to g(hA - hZ). It only depends on the difference in altitude of the ends A and Z, not on the path which connects A to Z. We have thus proven in the particular case of the gravity field on the surface of the Earth: Theorem: the work of the gravitational force does not depend on the path followed. If we neglect friction, the kinetic energy of a mobile on a roller coaster is the work of the gravitational force from initial rest. It only depends on the height difference , not on the path followed: File:Roller-coaster-car-loses-height-h-along-path.svg The work of a force can depend on the path followed. For example, the work of a friction force is greater as the path followed is longer. When a force field is such that the work of the force between two points does not depend on the path followed, we can introduce a potential. It is defined by choosing a point of zero potential. The potential at each point in space is then defined by the work of the force on a standard body between this point and the point of zero potential. For the force of gravity, we take as a standard a body whose mass is equal to one. For electric force, the standard is a body whose electric charge is equal to one. The potential is well defined because the work of the force does not depend on the path followed. Let WXY be the work of the force on a unit body moved from X to Y, VX the potential at point X and O a point of zero potential. By definition of V, VA = WAO and VB = WBO. So VA - VB = WAO - WBO. Or WAO = WAB + WBO. So VA - VB = WAB. The potential difference between two points is therefore always equal to the work of the force on a unit body displaced between these two points. The electric voltage between two points is the work of the electric force on a unit of charge moved between these two points. In steady state, the work of the electric force does not depend on the path followed, this force therefore derives from a potential. The electric voltage is then a potential difference. It is for the electric force what the difference in altitude is for gravity. The unit of electric charge is the Coulomb. One Volt (V) is one Joule (J) per Coulomb (C). This is the potential difference necessary to give a charge of one Coulomb an energy of one Joule. 1 V = 1 J/C When an electric voltage is imposed across a metal wire, an electric current passes through the wire, which is a current of electrons. The electrons are accelerated by the electric force, but their average kinetic energy does not increase, because they are slowed down by the metal. They lose by heating the metal all the energy they gained, through the Joule effect. Electric light was invented by heating a metal wire carrying an electric current to white heat. The electrical resistance of a material measures its ability to slow down electrons or ions passing through it.