Potentiel électrique
English
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개요
Source : Yong P. Chen, PhD, département de physique & astronomie, Faculté des sciences, Université de Purdue, West Lafayette, Indiana
Potentiel électrique, également connu sous le nom de « tension », mesure l’énergie potentielle électrique par charge d’unité. Champ électrique est une grandeur scalaire et est fondamental pour de nombreux effets électriques. Comme l’énergie potentielle, ce qui est physiquement significatif est la différence dans le potentiel électrique. Par exemple, la variation spatiale du potentiel électrique est liée au champ électrique, qui donne lieu à la force électrique sur une charge. La différence de potentiel électrique entre deux points dans une résistance entraîne l’écoulement du courant électrique.
Cette expérience utilisera aussi bien un voltmètre et un tube fluorescent pour démontrer le potentiel électrique (plus précisément, la différence de potentiel entre deux points dans l’espace) généré par une sphère chargée. L’expérience démontrera la notion de surfaces équipotentielles, qui sont perpendiculaires aux champs électriques.
Principles
Une charge ponctuelle Q située à l’origine (r = 0) produit un potentiel électrique :
(Équation 1)
à n’importe quel point dans l’espace avec une distance r de l’accusation (à l’origine r = 0). Équation 1 décrit également le potentiel électrique produit par une sphère uniformément chargée (centrée à r = 0) avec une charge totale Q dans l’espace en dehors de la sphère (Figure 1). Dans les deux cas, le point de « référence » (où le potentiel est zéro) est à la distance infinie de l’accusation. Le potentiel électrique varie le long de la direction radiale, ce qui est de la direction du champ électrique.
Pour deux points P1 et P2 avec distance r1 et r2 loin de l’origine (Centre de l’accusation), respectivement, la différence de potentiel entre ces deux points est :
(Équation 2)
Si le point P2 est à l’infini (→∞), ce qui réduit l’équation 2 à l’équation 1. Par conséquent, il y a une différence de potentiel entre deux points si et seulement si ces deux points ont une distance différente de l’origine (Centre de l’accusation). Une surface sphérique centrée à l’origine est une « surface équipotentielle » dans ce cas. Remarque dans ce cas, que le champ électrique (dans le sens radial) est perpendiculaire à la surface équipotentielle (sphère). Cela s’avère être vrai en général : la surface équipotentielle est perpendiculaire à la direction du champ électrique.
Figure 1 : Schéma montrant une sphère chargée reliée à un générateur électrique. Un voltmètre sert à mesurer le potentiel électrique en un point « A » (avec la distance r du centre de la sphère).
Procedure
Results
In steps 1.4-1.5, the voltmeter can be observed to give similar readings if the probe tip is kept at similar distances from the origin (that is, on an equipotential surface). However, the voltage drops if the probe moves farther away from the origin. The voltage reading at 1 m and 1.5 m away will be about 1/2 and 1/3 of the reading at 0.5 m away, respectively. If the voltage V measured versus the inverse distance (1/r) is plotted, a straight line results, as expected from Equation 1.
Applications and Summary
Electric potential (voltage) is ubiquitous and perhaps the most commonly used quantity in electricity. It is often much more convenient to use electric potential (which is a scalar) than electric field (which is a vector), even though the two can be related to each other. Electric potential difference is used to drive and control charge motion (accelerate/decelerate/deflect charges), for example in a TV screen or electron microscope. Electric potential difference (what we usually call voltage) is also what drives current flow in a conductor. Whenever one measures a voltage, one is measuring the electric potential difference between two points (one of which is sometimes a reference point or ground defined to have zero potential).
The author of the experiment acknowledges the assistance of Gary Hudson for material preparation and Chuanhsun Li for demonstrating the steps in the video.
내레이션 대본
Electric potential defines the energy of a charged particle. It gives rise to electric field and electric force, and is the basis of many electrical phenomena.
The term electrical potential is denoted by the Greek symbol Φ. It is a scalar quantity with a sign and magnitude. Any charge creates electric potential in the space around it. It is different from the term Voltage, although both these physical quantities are measured in Volts.
Here, we will first explain what these terms are, discuss the parameters that affect Φ, and then demonstrate the measurement of electric potential around a charged sphere.
As discussed in the Energy and Work video, potential energy of any object of mass m under the influence of gravitational acceleration g is equal to the amount of work needed to move that object by a height h from the ground. Mathematically, it is given by the formula mgh and has the unit of Joules.
Similarly, in the electric field E around a positively charged surface, the electrical potential energy at a specific point relative to a reference point is the amount of work necessary to move a positive test charge +q from the reference to that specific point. The distance between the two points is denoted by the letter d. Analogous to the gravitational potential energy, the electrical potential energy is the product of q, E, and d, and has the units of Joules.
Then, the electric potential or Φ at that point in the field is the electrical potential energy divided by ‘q’, the charge on the test charge. Therefore, the unit for Φ is joules per coulomb, AKA volts.
Now, if we consider another point in the field, it would have a different electric potential; say Φ0. The potential difference or Φdiff between the two points is known as voltage. This is the concept behind a battery, where the positive terminal is at a higher electric potential compared to the negative terminal and the difference between the two potentials is the voltage of the battery.
Coming back to electric potential, recall that it is a scalar quantity with a sign and magnitude. The sign depends on the source charge. Around an isolated positive charge, the potential is positive, whereas around an isolated negative charge it is negative.
The magnitude of the potential depends on the Q of the source charge producing the electric field, the distance d from the source charge, and the configuration.
For example, the electric potential at any given point around a point charge or a uniformly charged positive sphere with charge Q is given by this formula. It is evident that Φ is inversely proportional to the distance from the sphere. And the graph of electric potential magnitude versus distance is approaching zero at infinity.
This dependence on d also indicates that all locations at the same radius from the charged sphere would have the same potential. This means that there are equipotential surfaces of spherical shape around a charged sphere.
Now that we’ve explained the concepts behind electric potential and potential difference, let’s see how to validate these principles experimentally using a charged sphere.
This experiment uses a Van der Graff generator to charge a metal sphere. Connect the negative terminal of a voltmeter to the generator’s reference terminal or ground. Use a cable to connect the positive terminal of the voltmeter to a probe tip.
Turn the crank of the generator at least 10 times to charge the sphere then turn on the voltmeter and place the tip of the voltage probe about one-half meter away from the center of the sphere. Record the voltage reading at this location.
Move the probe tip around the sphere while maintaining a constant radius of one half meter from the center. During this time, observe the voltmeter measurements and note how the reading remains constant, indicating a spherical equipotential surface.
Repeat this procedure with the probe tip at a distance of one meter, and then one and a half meters from the center of the sphere.
The plot of measured potential versus distance displays a curve that decreases inversely with distance, which validates the theoretical relationship between electric potential and distance, for a charged sphere.
Electric potential is one of the most commonly used electrical quantities and is fundamental to the storage and release of electrical energy.
An electron microscope uses a high electric potential difference to accelerate electrons in a beam that bombards the sample under examination. These electrons act like a light in an optical microscope, but with much smaller wavelengths and much greater spatial resolution, enabling the ability to visualize sub-micron sized structures.
Electric potential is an important component of gel electrophoresis – a molecular biology technique commonly used for separating large molecules, such as DNA, by size and charge. In this technique, sample material is placed on a slab of agarose gel and an electric potential difference is applied between the ends. In the resulting electric field, the various molecules and molecular fragments move with speeds that depend on charge and molecular weight.
You’ve just watched JoVE’s introduction to electric potential. You should now know how to measure electric potential, and understand how it affects charges and relates to electric potential energy. Thanks for watching!